Solving LinkedIn Patches by Linear Optimization Rodrigo Celso de Lima Porto April 10, 2026
How to Play Patches ¶ Pathes is a game adapted from Shikaku (四角に切れ, shikaku ni kire ), a japanese puzzle created by the puzzle-specialized publisher Nikoli on 2011.
Shikaku is played on a grid. Some of the squares on the grid contain numbers. The goal is to divide the grid into rectangular pieces such that each piece contains exactly one number, and each number represents the area of
Figure 1: Example of a Shikaku grid. Source: Shikaku of the Day
Figure 2: Solution of a Shikaku example. Source: Shikaku of the Day
The Patches’ grid contains some colored patch seeds that may state some features about the rectangles to be drawn on the grid, such as the required area (optional) or required shape (which can be a vertical rectangle, a horizontal rectangle, a square or any shape).
Figure 3: Example of Patches mini game. Source: LinkedIn Patches
Objective Partition the grid into non-overlapping rectangular patches so that each patch meets the prescriptions on their respective seeds. Rules Each seed must be covered by only one patch that attends its prescriptions; A patch must cover only one seed; Specifically for the Patches game, the area of × \times × Problem Modeling ¶ Ranges ¶ Basically, we’ll have three ranges for defining all the next components: a range for rows, columns and ractangles.
I = { 1 , ⋯ , m } I = \{1, \cdots, m\} I = { 1 , ⋯ , m } The row range, where m m m J = { 1 , ⋯ , n } J = \{1, \cdots, n\} J = { 1 , ⋯ , n } The column range, where n n n K = { 1 , ⋯ , p } K = \{1, \cdots, p\} K = { 1 , ⋯ , p } Range of all patches to be drawn on grid game, where p p p Sets ¶ From I I I J J J K K K
S = I × J = { ( i , j ) ∣ ∀ i ∈ I , ∀ j ∈ J } S = I \times J = \{(i,j) \mid \forall i \in I, \forall j \in J\} S = I × J = {( i , j ) ∣ ∀ i ∈ I , ∀ j ∈ J } Set of all grid squares, that is just the Cartesian product between sets I I I J J J E = { ( i , j , k ) ∣ i ∈ I , j ∈ J , k ∈ K } ⊂ I × J × K E = \{(i,j,k) \mid i \in I, j \in J, k \in K\} \subset I \times J \times K E = {( i , j , k ) ∣ i ∈ I , j ∈ J , k ∈ K } ⊂ I × J × K Set of all squares ( i , j ) (i,j) ( i , j ) k k k V ⊆ K V \subseteq K V ⊆ K Set of required vertical patches, i. e., patches whose height is greater than its width. H ⊆ K H \subseteq K H ⊆ K Set of required horizontal patches, i. e., patches whose width is greater than its height. Q ⊆ K Q \subseteq K Q ⊆ K Set of required square patches, i. e., patches whose width is equal to its height. A ⊆ K A \subseteq K A ⊆ K Set of patches with a required area a k a_k a k Decision Variables ¶ For Patches game, it’ll have seven sets of decision varibles.
Integer Variables ¶ The following integer variables will be used to define the position and dimensions of the patches, which are the set of variables that solves the game:
l k ∈ I , ∀ k ∈ K l_k \in I, \forall k \in K l k ∈ I , ∀ k ∈ K Index of the leftmost column of the patch k k k t k ∈ J , ∀ k ∈ K t_k \in J, \forall k \in K t k ∈ J , ∀ k ∈ K Index of the top row of the patch k k k w k ∈ I , ∀ k ∈ K w_k \in I, \forall k \in K w k ∈ I , ∀ k ∈ K Width of the patch k k k h k ∈ J , ∀ k ∈ K h_k \in J, \forall k \in K h k ∈ J , ∀ k ∈ K Height of the patch k k k Binary Variables ¶ However, in order to ensure the rectangularity and continuity of the geometric shapes and their required areas, it is necessary to use the following auxiliary binary variables:
u i k ∈ { 0 , 1 } , ∀ ( i , k ) ∈ I × K u_{ik} \in \B, \forall (i,k) \in I \times K u ik ∈ { 0 , 1 } , ∀ ( i , k ) ∈ I × K u i k = 1 u_{ik} = 1 u ik = 1 i i i k k k u i k = 0 u_{ik} = 0 u ik = 0 v j k ∈ { 0 , 1 } , ∀ ( j , k ) ∈ J × K v_{jk} \in \B, \forall (j,k) \in J \times K v jk ∈ { 0 , 1 } , ∀ ( j , k ) ∈ J × K v j k = 1 v_{jk} = 1 v jk = 1 j j j k k k v j k = 0 v_{jk} = 0 v jk = 0 x i j k ∈ { 0 , 1 } , ∀ ( i , j , k ) ∈ I × J × K x_{ijk} \in \B, \forall (i,j,k) \in I \times J \times K x ijk ∈ { 0 , 1 } , ∀ ( i , j , k ) ∈ I × J × K x i j k = 1 x_{ijk} = 1 x ijk = 1 ( i , j ) (i,j) ( i , j ) k k k x i j k = 0 x_{ijk} = 0 x ijk = 0 Further on, we’ll put constraints that links the variables x i j k x_{ijk} x ijk u i k u_{ik} u ik v j k v_{jk} v jk i i i j j j k k k ( i , j ) (i,j) ( i , j ) k k k u i k = 0 u_{ik}=0 u ik = 0 v j k = 0 v_{jk}=0 v jk = 0 x i j k x_{ijk} x ijk ( i , j ) (i,j) ( i , j )
Parameters ¶ a k ∈ N a_k \in \N a k ∈ N Required area for the patch k ∈ A k \in A k ∈ A Objective Function ¶ Since we only want to find a solution that satisfies all the rules of the game, the objective function of Patches’ model is a constant. Therefore, the LOP is a feasibility problem, whose objective function consists of maximizing (or minimizing) an arbitrary constant.
Constraints ¶ Domain Constraints First, let’s settle the sets of constraints for the domain of decision variables.
Integrity Constraints The main decision variables must be integers. l k ∈ N , ∀ k ∈ K l_k \in \N, \forall k \in K l k ∈ N , ∀ k ∈ K t k ∈ N , ∀ k ∈ K t_k \in \N, \forall k \in K t k ∈ N , ∀ k ∈ K w k ∈ N , ∀ k ∈ K w_k \in \N, \forall k \in K w k ∈ N , ∀ k ∈ K h k ∈ N , ∀ k ∈ K h_k \in \N, \forall k \in K h k ∈ N , ∀ k ∈ K Binarity Constraints The auxiliary decision variables must be binary. u i k ∈ { 0 , 1 } , ∀ ( i , k ) ∈ I × K u_{ik} \in \B, \forall (i,k) \in I \times K u ik ∈ { 0 , 1 } , ∀ ( i , k ) ∈ I × K v j k ∈ { 0 , 1 } , ∀ ( j , k ) ∈ J × K v_{jk} \in \B, \forall (j,k) \in J \times K v jk ∈ { 0 , 1 } , ∀ ( j , k ) ∈ J × K x i j k ∈ { 0 , 1 } , ∀ ( i , j , k ) ∈ I × J × K x_{ijk} \in \B, \forall (i,j,k) \in I \times J \times K x ijk ∈ { 0 , 1 } , ∀ ( i , j , k ) ∈ I × J × K Unique-Patch-Per-Square Constraints Each grid square ( i , j ) (i,j) ( i , j ) k k k
∑ k ∈ K x i j k = 1 , ∀ ( i , j ) ∈ S \sum_{k \in K}{x_{ijk}} = 1, \forall (i,j) \in S k ∈ K ∑ x ijk = 1 , ∀ ( i , j ) ∈ S Grid-Boundaries Constraints These sets of constraints ensure that any patch k k k
Top-Row-Position Constraints For each patch k k k t k t_k t k t k ≥ 1 , ∀ k ∈ K t_k \ge 1, \forall k \in K t k ≥ 1 , ∀ k ∈ K Bottom-Row-Position Constraints For each patch k k k t k + h k − 1 t_k + h_k - 1 t k + h k − 1 n n n t k + h k − 1 ≤ n , ∀ k ∈ K t_k + h_k - 1 \le n, \forall k \in K t k + h k − 1 ≤ n , ∀ k ∈ K Leftmost-Column-Position Constraints For each patch k k k l k l_k l k l k ≥ 1 , ∀ k ∈ K l_k \ge 1, \forall k \in K l k ≥ 1 , ∀ k ∈ K Rightmost-Column-Position Constraints For each patch k k k l k + w k − 1 l_k + w_k - 1 l k + w k − 1 m m m l k + w k − 1 ≤ m , ∀ k ∈ K l_k + w_k - 1 \le m, \forall k \in K l k + w k − 1 ≤ m , ∀ k ∈ K Patch-Boundaries Constraints These sets of constraints uses the Big M M M i i i j j j k k k
Top-Boundary Constraints if a row i i i k k k i i i t k t_k t k t k − i ≤ M ( 1 − u i k ) , ∀ ( i , k ) ∈ I × K t_k - i \le M(1 - u_{ik}), \forall (i,k) \in I \times K t k − i ≤ M ( 1 − u ik ) , ∀ ( i , k ) ∈ I × K Bottom-Boundary Constraints if a square ( i , j ) (i,j) ( i , j ) k k k i i i t k + h k − 1 t_k + h_k - 1 t k + h k − 1 i − ( t k + h k − 1 ) ≤ M ( 1 − u i k ) , ∀ ( i , k ) ∈ I × K i - (t_k + h_k - 1) \le M(1 - u_{ik}), \forall (i,k) \in I \times K i − ( t k + h k − 1 ) ≤ M ( 1 − u ik ) , ∀ ( i , k ) ∈ I × K Leftmost-Boundary Constraints if a colum j j j k k k j j j l k l_k l k l k − j ≤ M ( 1 − v j k ) , ∀ ( j , k ) ∈ J × K l_k - j \le M(1 - v_{jk}), \forall (j,k) \in J \times K l k − j ≤ M ( 1 − v jk ) , ∀ ( j , k ) ∈ J × K Rightmost-Boundary Constraints if a colum j j j k k k j j j l k + w k − 1 l_k + w_k - 1 l k + w k − 1 j − ( l k + w k − 1 ) ≤ M ( 1 − v j k ) , ∀ ( j , k ) ∈ J × K j - (l_k + w_k - 1) \le M(1 - v_{jk}), \forall (j,k) \in J \times K j − ( l k + w k − 1 ) ≤ M ( 1 − v jk ) , ∀ ( j , k ) ∈ J × K The last set of constraints ensures that, if u i k = 1 u_{ik} = 1 u ik = 1 i i i k k k v j k v_{jk} v jk i i i k k k u i k = 0 u_{ik}=0 u ik = 0 u i k u_{ik} u ik k k k h k h_k h k v j k v_{jk} v jk k k k w k w_k w k
Patch Dimensions constraints These constraints are important to ensure that there’ll not be any gap inside the patches.
Height Constraints The sum of all selected rows u i k u_{ik} u ik k k k ∑ i ∈ I u i k = h k , ∀ k ∈ K \sum_{i \in I}{u_{ik}} = h_k, \forall k \in K i ∈ I ∑ u ik = h k , ∀ k ∈ K Width Constraints The sum of all selected columns v j k v_{jk} v jk k k k ∑ j ∈ J v j k = w k , ∀ k ∈ K \sum_{j \in J}{v_{jk}} = w_k, \forall k \in K j ∈ J ∑ v jk = w k , ∀ k ∈ K McCormick Linearization Constraints These sets of constraints translates the non-linear contraint x i j k = u i k × v j k x_{ijk} = u_{ik} \times v_{jk} x ijk = u ik × v jk i i i j j j k k k ( i , j ) (i,j) ( i , j ) k k k u i k = 0 u_{ik}=0 u ik = 0 v j k = 0 v_{jk}=0 v jk = 0 x i j k x_{ijk} x ijk ( i , j ) (i,j) ( i , j )
Cutout-Row Constraints If a row i i i k k k ∑ j ∈ J x i j k ≤ n ⋅ u i k , ∀ ( i , k ) ∈ I × K \sum_{j \in J}{x_{ijk}} \le n \cdot u_{ik}, \forall (i,k) \in I \times K j ∈ J ∑ x ijk ≤ n ⋅ u ik , ∀ ( i , k ) ∈ I × K Cutout-Column Constraints If a column j j j k k k ∑ i ∈ I x i j k ≤ m ⋅ v j k , ∀ ( j , k ) ∈ J × K \sum_{i \in I}{x_{ijk}} \le m \cdot v_{jk}, \forall (j,k) \in J \times K i ∈ I ∑ x ijk ≤ m ⋅ v jk , ∀ ( j , k ) ∈ J × K Square-Activator Constraints If both row i i i j j j k k k x i j k ≥ u i k + v j k − 1 , ∀ ( i , j , k ) ∈ I × J × K x_{ijk} \ge u_{ik} + v_{jk} - 1, \forall (i,j,k) \in I \times J \times K x ijk ≥ u ik + v jk − 1 , ∀ ( i , j , k ) ∈ I × J × K Seed Square Constraints These sets of constraints deal with prescriptions required by the seed squares.
Seed Square Coverage Constraints For each square ( i , j ) (i,j) ( i , j ) k k k k k k x i j k = 1 , ∀ ( i , j , k ) ∈ T x_{ijk} = 1, \forall (i,j,k) \in T x ijk = 1 , ∀ ( i , j , k ) ∈ T Area Constraints For each patch k k k a k a_k a k x i j k x_{ijk} x ijk a k a_k a k ∑ ( i , j ) ∈ S x i j k = a k , ∀ k ∈ A \sum_{(i,j) \in S}{x_{ijk}} = a_k, \forall k \in A ( i , j ) ∈ S ∑ x ijk = a k , ∀ k ∈ A Vertical Patch Constraints For each vertical patch k k k h k h_k h k w k w_k w k w k < h k , ∀ k ∈ V w_k < h_k, \forall k \in V w k < h k , ∀ k ∈ V Horizontal Patch Constraints For each horizontal patch k k k w k w_k w k h k h_k h k w k > h k , ∀ k ∈ H w_k > h_k, \forall k \in H w k > h k , ∀ k ∈ H Square Patch Constraints For each square patch k k k w k w_k w k h k h_k h k w k = h k , ∀ k ∈ Q w_k = h_k, \forall k \in Q w k = h k , ∀ k ∈ Q Abstract Model ¶ With all components defined, we have the following abstract model for Patches game:
Min C \text{Min } \ C Min C S.t.: x i j k ≥ u i k + v j k − 1 , ∀ ( i , j , k ) ∈ I × J × K t k ≥ 1 , ∀ k ∈ K t k + h k − 1 ≤ n , ∀ k ∈ K l k ≥ 1 , ∀ k ∈ K l k + w k − 1 ≤ m , ∀ k ∈ K t k − i ≤ m ( 1 − u i k ) , ∀ ( i , k ) ∈ I × K i − ( t k + h k − 1 ) ≤ m ( 1 − u i k ) , ∀ ( i , k ) ∈ I × K l k − j ≤ n ( 1 − v j k ) , ∀ ( j , k ) ∈ J × K j − ( l k + w k − 1 ) ≤ n ( 1 − v j k ) , ∀ ( j , k ) ∈ J × K ∑ i ∈ I u i k = h k , ∀ k ∈ K ∑ j ∈ J v j k = w k , ∀ k ∈ K ∑ k ∈ K x i j k = 1 , ∀ ( i , j ) ∈ S ∑ j ∈ J x i j k ≤ n u i k , ∀ ( i , k ) ∈ I × K ∑ i ∈ I x i j k ≤ m v j k , ∀ ( j , k ) ∈ J × K x i j k = 1 , ∀ ( i , j , k ) ∈ E ∑ ( i , j ) ∈ S x i j k = a k , ∀ k ∈ A w k < h k , ∀ k ∈ V w k > h k , ∀ k ∈ H w k = h k , ∀ k ∈ Q l k ∈ N , ∀ k ∈ K t k ∈ N , ∀ k ∈ K w k ∈ N , ∀ k ∈ K h k ∈ N , ∀ k ∈ K u i j ∈ { 0 , 1 } , ∀ ( i , k ) ∈ I × K v j k ∈ { 0 , 1 } , ∀ ( j , k ) ∈ J × K x i j k ∈ { 0 , 1 } , ∀ ( i , j , k ) ∈ I × J × K \begin{array}{rll}
\text{S.t.:} & & \\
& x_{ijk} \ge u_{ik} + v_{jk} - 1, & \forall (i,j,k) \in I \times J \times K \\
& t_k \ge 1, & \forall k \in K \\
& t_k + h_k - 1 \le n, & \forall k \in K \\
& l_k \ge 1, & \forall k \in K \\
& l_k + w_k - 1 \le m, & \forall k \in K \\
& t_k - i \le m(1-u_{ik}), & \forall (i,k) \in I \times K \\
& i - (t_k + h_k - 1) \le m(1-u_{ik}), & \forall (i,k) \in I \times K \\
& l_k - j \le n(1-v_{jk}), & \forall (j,k) \in J \times K \\
& j - (l_k + w_k - 1) \le n(1-v_{jk}), & \forall (j,k) \in J \times K \\
& \sum_{i \in I}{u_{ik}} = h_k, & \forall k \in K \\
& \sum_{j \in J}{v_{jk}} = w_k, & \forall k \in K \\
& \sum_{k \in K}{x_{ijk}} = 1, & \forall (i,j) \in S \\
& \sum_{j \in J}{x_{ijk}} \le nu_{ik}, & \forall (i,k) \in I \times K \\
& \sum_{i \in I}{x_{ijk}} \le mv_{jk}, & \forall (j,k) \in J \times K \\
& x_{ijk} = 1, & \forall (i,j,k) \in E \\
& \sum_{(i,j) \in S}{x_{ijk}} = a_k, & \forall k \in A \\
& w_k < h_k, & \forall k \in V \\
& w_k > h_k, & \forall k \in H \\
& w_k = h_k, & \forall k \in Q \\
& l_k \in \N, & \forall k \in K \\
& t_k \in \N, & \forall k \in K \\
& w_k \in \N, & \forall k \in K \\
& h_k \in \N, & \forall k \in K \\
& u_{ij} \in \B, & \forall (i,k) \in I \times K \\
& v_{jk} \in \B, & \forall (j,k) \in J \times K \\
& x_{ijk} \in \B, & \forall (i,j,k) \in I \times J \times K \\
\end{array} S.t.: x ijk ≥ u ik + v jk − 1 , t k ≥ 1 , t k + h k − 1 ≤ n , l k ≥ 1 , l k + w k − 1 ≤ m , t k − i ≤ m ( 1 − u ik ) , i − ( t k + h k − 1 ) ≤ m ( 1 − u ik ) , l k − j ≤ n ( 1 − v jk ) , j − ( l k + w k − 1 ) ≤ n ( 1 − v jk ) , ∑ i ∈ I u ik = h k , ∑ j ∈ J v jk = w k , ∑ k ∈ K x ijk = 1 , ∑ j ∈ J x ijk ≤ n u ik , ∑ i ∈ I x ijk ≤ m v jk , x ijk = 1 , ∑ ( i , j ) ∈ S x ijk = a k , w k < h k , w k > h k , w k = h k , l k ∈ N , t k ∈ N , w k ∈ N , h k ∈ N , u ij ∈ { 0 , 1 } , v jk ∈ { 0 , 1 } , x ijk ∈ { 0 , 1 } , ∀ ( i , j , k ) ∈ I × J × K ∀ k ∈ K ∀ k ∈ K ∀ k ∈ K ∀ k ∈ K ∀ ( i , k ) ∈ I × K ∀ ( i , k ) ∈ I × K ∀ ( j , k ) ∈ J × K ∀ ( j , k ) ∈ J × K ∀ k ∈ K ∀ k ∈ K ∀ ( i , j ) ∈ S ∀ ( i , k ) ∈ I × K ∀ ( j , k ) ∈ J × K ∀ ( i , j , k ) ∈ E ∀ k ∈ A ∀ k ∈ V ∀ k ∈ H ∀ k ∈ Q ∀ k ∈ K ∀ k ∈ K ∀ k ∈ K ∀ k ∈ K ∀ ( i , k ) ∈ I × K ∀ ( j , k ) ∈ J × K ∀ ( i , j , k ) ∈ I × J × K Concrete model ¶ The Patches game to be solved will be the No. 16, published on April 2nd , 2026.
Figure 4: Patches problem instance used in this article. Source: LinkedIn Patches
And you concrete model is as the following:
S.t. :
Unique-Patch-Per-Square Constraints x 11 ■ + x 11 ■ + x 11 ■ + x 11 ■ + x 11 ■ + x 11 ■ + x 11 ■ + x 11 ■ + x 11 ■ + x 11 ■ = 1 x_{11\yellowbox} + x_{11\tealbox} + x_{11\purplebox} + x_{11\greenbox} + x_{11\orangebox} + x_{11\redbox} + x_{11\bluebox} + x_{11\magentabox} + x_{11\brickbox} + x_{11\brownbox} = 1 x 11 ■ + x 11 ■ + x 11 ■ + x 11 ■ + x 11 ■ + x 11 ■ + x 11 ■ + x 11 ■ + x 11 ■ + x 11 ■ = 1 Square (1,1) x 12 ■ + x 12 ■ + x 12 ■ + x 12 ■ + x 12 ■ + x 12 ■ + x 12 ■ + x 12 ■ + x 12 ■ + x 12 ■ = 1 x_{12\yellowbox} + x_{12\tealbox} + x_{12\purplebox} + x_{12\greenbox} + x_{12\orangebox} + x_{12\redbox} + x_{12\bluebox} + x_{12\magentabox} + x_{12\brickbox} + x_{12\brownbox} = 1 x 12 ■ + x 12 ■ + x 12 ■ + x 12 ■ + x 12 ■ + x 12 ■ + x 12 ■ + x 12 ■ + x 12 ■ + x 12 ■ = 1 Square (1,2) x 13 ■ + x 13 ■ + x 13 ■ + x 13 ■ + x 13 ■ + x 13 ■ + x 13 ■ + x 13 ■ + x 13 ■ + x 13 ■ = 1 x_{13\yellowbox} + x_{13\tealbox} + x_{13\purplebox} + x_{13\greenbox} + x_{13\orangebox} + x_{13\redbox} + x_{13\bluebox} + x_{13\magentabox} + x_{13\brickbox} + x_{13\brownbox} = 1 x 13 ■ + x 13 ■ + x 13 ■ + x 13 ■ + x 13 ■ + x 13 ■ + x 13 ■ + x 13 ■ + x 13 ■ + x 13 ■ = 1 Square (1,3) x 14 ■ + x 14 ■ + x 14 ■ + x 14 ■ + x 14 ■ + x 14 ■ + x 14 ■ + x 14 ■ + x 14 ■ + x 14 ■ = 1 x_{14\yellowbox} + x_{14\tealbox} + x_{14\purplebox} + x_{14\greenbox} + x_{14\orangebox} + x_{14\redbox} + x_{14\bluebox} + x_{14\magentabox} + x_{14\brickbox} + x_{14\brownbox} = 1 x 14 ■ + x 14 ■ + x 14 ■ + x 14 ■ + x 14 ■ + x 14 ■ + x 14 ■ + x 14 ■ + x 14 ■ + x 14 ■ = 1 Square (1,4) x 15 ■ + x 15 ■ + x 15 ■ + x 15 ■ + x 15 ■ + x 15 ■ + x 15 ■ + x 15 ■ + x 15 ■ + x 15 ■ = 1 x_{15\yellowbox} + x_{15\tealbox} + x_{15\purplebox} + x_{15\greenbox} + x_{15\orangebox} + x_{15\redbox} + x_{15\bluebox} + x_{15\magentabox} + x_{15\brickbox} + x_{15\brownbox} = 1 x 15 ■ + x 15 ■ + x 15 ■ + x 15 ■ + x 15 ■ + x 15 ■ + x 15 ■ + x 15 ■ + x 15 ■ + x 15 ■ = 1 Square (1,5) x 16 ■ + x 16 ■ + x 16 ■ + x 16 ■ + x 16 ■ + x 16 ■ + x 16 ■ + x 16 ■ + x 16 ■ + x 16 ■ = 1 x_{16\yellowbox} + x_{16\tealbox} + x_{16\purplebox} + x_{16\greenbox} + x_{16\orangebox} + x_{16\redbox} + x_{16\bluebox} + x_{16\magentabox} + x_{16\brickbox} + x_{16\brownbox} = 1 x 16 ■ + x 16 ■ + x 16 ■ + x 16 ■ + x 16 ■ + x 16 ■ + x 16 ■ + x 16 ■ + x 16 ■ + x 16 ■ = 1 Square (1,6) x 21 ■ + x 21 ■ + x 21 ■ + x 21 ■ + x 21 ■ + x 21 ■ + x 21 ■ + x 21 ■ + x 21 ■ + x 21 ■ = 1 x_{21\yellowbox} + x_{21\tealbox} + x_{21\purplebox} + x_{21\greenbox} + x_{21\orangebox} + x_{21\redbox} + x_{21\bluebox} + x_{21\magentabox} + x_{21\brickbox} + x_{21\brownbox} = 1 x 21 ■ + x 21 ■ + x 21 ■ + x 21 ■ + x 21 ■ + x 21 ■ + x 21 ■ + x 21 ■ + x 21 ■ + x 21 ■ = 1 Square (2,1) x 22 ■ + x 22 ■ + x 22 ■ + x 22 ■ + x 22 ■ + x 22 ■ + x 22 ■ + x 22 ■ + x 22 ■ + x 22 ■ = 1 x_{22\yellowbox} + x_{22\tealbox} + x_{22\purplebox} + x_{22\greenbox} + x_{22\orangebox} + x_{22\redbox} + x_{22\bluebox} + x_{22\magentabox} + x_{22\brickbox} + x_{22\brownbox} = 1 x 22 ■ + x 22 ■ + x 22 ■ + x 22 ■ + x 22 ■ + x 22 ■ + x 22 ■ + x 22 ■ + x 22 ■ + x 22 ■ = 1 Square (2,2) x 23 ■ + x 23 ■ + x 23 ■ + x 23 ■ + x 23 ■ + x 23 ■ + x 23 ■ + x 23 ■ + x 23 ■ + x 23 ■ = 1 x_{23\yellowbox} + x_{23\tealbox} + x_{23\purplebox} + x_{23\greenbox} + x_{23\orangebox} + x_{23\redbox} + x_{23\bluebox} + x_{23\magentabox} + x_{23\brickbox} + x_{23\brownbox} = 1 x 23 ■ + x 23 ■ + x 23 ■ + x 23 ■ + x 23 ■ + x 23 ■ + x 23 ■ + x 23 ■ + x 23 ■ + x 23 ■ = 1 Square (2,3) x 24 ■ + x 24 ■ + x 24 ■ + x 24 ■ + x 24 ■ + x 24 ■ + x 24 ■ + x 24 ■ + x 24 ■ + x 24 ■ = 1 x_{24\yellowbox} + x_{24\tealbox} + x_{24\purplebox} + x_{24\greenbox} + x_{24\orangebox} + x_{24\redbox} + x_{24\bluebox} + x_{24\magentabox} + x_{24\brickbox} + x_{24\brownbox} = 1 x 24 ■ + x 24 ■ + x 24 ■ + x 24 ■ + x 24 ■ + x 24 ■ + x 24 ■ + x 24 ■ + x 24 ■ + x 24 ■ = 1 Square (2,4) x 25 ■ + x 25 ■ + x 25 ■ + x 25 ■ + x 25 ■ + x 25 ■ + x 25 ■ + x 25 ■ + x 25 ■ + x 25 ■ = 1 x_{25\yellowbox} + x_{25\tealbox} + x_{25\purplebox} + x_{25\greenbox} + x_{25\orangebox} + x_{25\redbox} + x_{25\bluebox} + x_{25\magentabox} + x_{25\brickbox} + x_{25\brownbox} = 1 x 25 ■ + x 25 ■ + x 25 ■ + x 25 ■ + x 25 ■ + x 25 ■ + x 25 ■ + x 25 ■ + x 25 ■ + x 25 ■ = 1 Square (2,5) x 26 ■ + x 26 ■ + x 26 ■ + x 26 ■ + x 26 ■ + x 26 ■ + x 26 ■ + x 26 ■ + x 26 ■ + x 26 ■ = 1 x_{26\yellowbox} + x_{26\tealbox} + x_{26\purplebox} + x_{26\greenbox} + x_{26\orangebox} + x_{26\redbox} + x_{26\bluebox} + x_{26\magentabox} + x_{26\brickbox} + x_{26\brownbox} = 1 x 26 ■ + x 26 ■ + x 26 ■ + x 26 ■ + x 26 ■ + x 26 ■ + x 26 ■ + x 26 ■ + x 26 ■ + x 26 ■ = 1 Square (2,6) x 31 ■ + x 31 ■ + x 31 ■ + x 31 ■ + x 31 ■ + x 31 ■ + x 31 ■ + x 31 ■ + x 31 ■ + x 31 ■ = 1 x_{31\yellowbox} + x_{31\tealbox} + x_{31\purplebox} + x_{31\greenbox} + x_{31\orangebox} + x_{31\redbox} + x_{31\bluebox} + x_{31\magentabox} + x_{31\brickbox} + x_{31\brownbox} = 1 x 31 ■ + x 31 ■ + x 31 ■ + x 31 ■ + x 31 ■ + x 31 ■ + x 31 ■ + x 31 ■ + x 31 ■ + x 31 ■ = 1 Square (3,1) x 32 ■ + x 32 ■ + x 32 ■ + x 32 ■ + x 32 ■ + x 32 ■ + x 32 ■ + x 32 ■ + x 32 ■ + x 32 ■ = 1 x_{32\yellowbox} + x_{32\tealbox} + x_{32\purplebox} + x_{32\greenbox} + x_{32\orangebox} + x_{32\redbox} + x_{32\bluebox} + x_{32\magentabox} + x_{32\brickbox} + x_{32\brownbox} = 1 x 32 ■ + x 32 ■ + x 32 ■ + x 32 ■ + x 32 ■ + x 32 ■ + x 32 ■ + x 32 ■ + x 32 ■ + x 32 ■ = 1 Square (3,2) x 33 ■ + x 33 ■ + x 33 ■ + x 33 ■ + x 33 ■ + x 33 ■ + x 33 ■ + x 33 ■ + x 33 ■ + x 33 ■ = 1 x_{33\yellowbox} + x_{33\tealbox} + x_{33\purplebox} + x_{33\greenbox} + x_{33\orangebox} + x_{33\redbox} + x_{33\bluebox} + x_{33\magentabox} + x_{33\brickbox} + x_{33\brownbox} = 1 x 33 ■ + x 33 ■ + x 33 ■ + x 33 ■ + x 33 ■ + x 33 ■ + x 33 ■ + x 33 ■ + x 33 ■ + x 33 ■ = 1 Square (3,3) x 34 ■ + x 34 ■ + x 34 ■ + x 34 ■ + x 34 ■ + x 34 ■ + x 34 ■ + x 34 ■ + x 34 ■ + x 34 ■ = 1 x_{34\yellowbox} + x_{34\tealbox} + x_{34\purplebox} + x_{34\greenbox} + x_{34\orangebox} + x_{34\redbox} + x_{34\bluebox} + x_{34\magentabox} + x_{34\brickbox} + x_{34\brownbox} = 1 x 34 ■ + x 34 ■ + x 34 ■ + x 34 ■ + x 34 ■ + x 34 ■ + x 34 ■ + x 34 ■ + x 34 ■ + x 34 ■ = 1 Square (3,4) x 35 ■ + x 35 ■ + x 35 ■ + x 35 ■ + x 35 ■ + x 35 ■ + x 35 ■ + x 35 ■ + x 35 ■ + x 35 ■ = 1 x_{35\yellowbox} + x_{35\tealbox} + x_{35\purplebox} + x_{35\greenbox} + x_{35\orangebox} + x_{35\redbox} + x_{35\bluebox} + x_{35\magentabox} + x_{35\brickbox} + x_{35\brownbox} = 1 x 35 ■ + x 35 ■ + x 35 ■ + x 35 ■ + x 35 ■ + x 35 ■ + x 35 ■ + x 35 ■ + x 35 ■ + x 35 ■ = 1 Square (3,5) x 36 ■ + x 36 ■ + x 36 ■ + x 36 ■ + x 36 ■ + x 36 ■ + x 36 ■ + x 36 ■ + x 36 ■ + x 36 ■ = 1 x_{36\yellowbox} + x_{36\tealbox} + x_{36\purplebox} + x_{36\greenbox} + x_{36\orangebox} + x_{36\redbox} + x_{36\bluebox} + x_{36\magentabox} + x_{36\brickbox} + x_{36\brownbox} = 1 x 36 ■ + x 36 ■ + x 36 ■ + x 36 ■ + x 36 ■ + x 36 ■ + x 36 ■ + x 36 ■ + x 36 ■ + x 36 ■ = 1 Square (3,6) x 41 ■ + x 41 ■ + x 41 ■ + x 41 ■ + x 41 ■ + x 41 ■ + x 41 ■ + x 41 ■ + x 41 ■ + x 41 ■ = 1 x_{41\yellowbox} + x_{41\tealbox} + x_{41\purplebox} + x_{41\greenbox} + x_{41\orangebox} + x_{41\redbox} + x_{41\bluebox} + x_{41\magentabox} + x_{41\brickbox} + x_{41\brownbox} = 1 x 41 ■ + x 41 ■ + x 41 ■ + x 41 ■ + x 41 ■ + x 41 ■ + x 41 ■ + x 41 ■ + x 41 ■ + x 41 ■ = 1 Square (4,1) x 42 ■ + x 42 ■ + x 42 ■ + x 42 ■ + x 42 ■ + x 42 ■ + x 42 ■ + x 42 ■ + x 42 ■ + x 42 ■ = 1 x_{42\yellowbox} + x_{42\tealbox} + x_{42\purplebox} + x_{42\greenbox} + x_{42\orangebox} + x_{42\redbox} + x_{42\bluebox} + x_{42\magentabox} + x_{42\brickbox} + x_{42\brownbox} = 1 x 42 ■ + x 42 ■ + x 42 ■ + x 42 ■ + x 42 ■ + x 42 ■ + x 42 ■ + x 42 ■ + x 42 ■ + x 42 ■ = 1 Square (4,2) x 43 ■ + x 43 ■ + x 43 ■ + x 43 ■ + x 43 ■ + x 43 ■ + x 43 ■ + x 43 ■ + x 43 ■ + x 43 ■ = 1 x_{43\yellowbox} + x_{43\tealbox} + x_{43\purplebox} + x_{43\greenbox} + x_{43\orangebox} + x_{43\redbox} + x_{43\bluebox} + x_{43\magentabox} + x_{43\brickbox} + x_{43\brownbox} = 1 x 43 ■ + x 43 ■ + x 43 ■ + x 43 ■ + x 43 ■ + x 43 ■ + x 43 ■ + x 43 ■ + x 43 ■ + x 43 ■ = 1 Square (4,3) x 44 ■ + x 44 ■ + x 44 ■ + x 44 ■ + x 44 ■ + x 44 ■ + x 44 ■ + x 44 ■ + x 44 ■ + x 44 ■ = 1 x_{44\yellowbox} + x_{44\tealbox} + x_{44\purplebox} + x_{44\greenbox} + x_{44\orangebox} + x_{44\redbox} + x_{44\bluebox} + x_{44\magentabox} + x_{44\brickbox} + x_{44\brownbox} = 1 x 44 ■ + x 44 ■ + x 44 ■ + x 44 ■ + x 44 ■ + x 44 ■ + x 44 ■ + x 44 ■ + x 44 ■ + x 44 ■ = 1 Square (4,4) x 45 ■ + x 45 ■ + x 45 ■ + x 45 ■ + x 45 ■ + x 45 ■ + x 45 ■ + x 45 ■ + x 45 ■ + x 45 ■ = 1 x_{45\yellowbox} + x_{45\tealbox} + x_{45\purplebox} + x_{45\greenbox} + x_{45\orangebox} + x_{45\redbox} + x_{45\bluebox} + x_{45\magentabox} + x_{45\brickbox} + x_{45\brownbox} = 1 x 45 ■ + x 45 ■ + x 45 ■ + x 45 ■ + x 45 ■ + x 45 ■ + x 45 ■ + x 45 ■ + x 45 ■ + x 45 ■ = 1 Square (4,5) x 46 ■ + x 46 ■ + x 46 ■ + x 46 ■ + x 46 ■ + x 46 ■ + x 46 ■ + x 46 ■ + x 46 ■ + x 46 ■ = 1 x_{46\yellowbox} + x_{46\tealbox} + x_{46\purplebox} + x_{46\greenbox} + x_{46\orangebox} + x_{46\redbox} + x_{46\bluebox} + x_{46\magentabox} + x_{46\brickbox} + x_{46\brownbox} = 1 x 46 ■ + x 46 ■ + x 46 ■ + x 46 ■ + x 46 ■ + x 46 ■ + x 46 ■ + x 46 ■ + x 46 ■ + x 46 ■ = 1 Square (4,6) x 51 ■ + x 51 ■ + x 51 ■ + x 51 ■ + x 51 ■ + x 51 ■ + x 51 ■ + x 51 ■ + x 51 ■ + x 51 ■ = 1 x_{51\yellowbox} + x_{51\tealbox} + x_{51\purplebox} + x_{51\greenbox} + x_{51\orangebox} + x_{51\redbox} + x_{51\bluebox} + x_{51\magentabox} + x_{51\brickbox} + x_{51\brownbox} = 1 x 51 ■ + x 51 ■ + x 51 ■ + x 51 ■ + x 51 ■ + x 51 ■ + x 51 ■ + x 51 ■ + x 51 ■ + x 51 ■ = 1 Square (5,1) x 52 ■ + x 52 ■ + x 52 ■ + x 52 ■ + x 52 ■ + x 52 ■ + x 52 ■ + x 52 ■ + x 52 ■ + x 52 ■ = 1 x_{52\yellowbox} + x_{52\tealbox} + x_{52\purplebox} + x_{52\greenbox} + x_{52\orangebox} + x_{52\redbox} + x_{52\bluebox} + x_{52\magentabox} + x_{52\brickbox} + x_{52\brownbox} = 1 x 52 ■ + x 52 ■ + x 52 ■ + x 52 ■ + x 52 ■ + x 52 ■ + x 52 ■ + x 52 ■ + x 52 ■ + x 52 ■ = 1 Square (5,2) x 53 ■ + x 53 ■ + x 53 ■ + x 53 ■ + x 53 ■ + x 53 ■ + x 53 ■ + x 53 ■ + x 53 ■ + x 53 ■ = 1 x_{53\yellowbox} + x_{53\tealbox} + x_{53\purplebox} + x_{53\greenbox} + x_{53\orangebox} + x_{53\redbox} + x_{53\bluebox} + x_{53\magentabox} + x_{53\brickbox} + x_{53\brownbox} = 1 x 53 ■ + x 53 ■ + x 53 ■ + x 53 ■ + x 53 ■ + x 53 ■ + x 53 ■ + x 53 ■ + x 53 ■ + x 53 ■ = 1 Square (5,3) x 54 ■ + x 54 ■ + x 54 ■ + x 54 ■ + x 54 ■ + x 54 ■ + x 54 ■ + x 54 ■ + x 54 ■ + x 54 ■ = 1 x_{54\yellowbox} + x_{54\tealbox} + x_{54\purplebox} + x_{54\greenbox} + x_{54\orangebox} + x_{54\redbox} + x_{54\bluebox} + x_{54\magentabox} + x_{54\brickbox} + x_{54\brownbox} = 1 x 54 ■ + x 54 ■ + x 54 ■ + x 54 ■ + x 54 ■ + x 54 ■ + x 54 ■ + x 54 ■ + x 54 ■ + x 54 ■ = 1 Square (5,4) x 55 ■ + x 55 ■ + x 55 ■ + x 55 ■ + x 55 ■ + x 55 ■ + x 55 ■ + x 55 ■ + x 55 ■ + x 55 ■ = 1 x_{55\yellowbox} + x_{55\tealbox} + x_{55\purplebox} + x_{55\greenbox} + x_{55\orangebox} + x_{55\redbox} + x_{55\bluebox} + x_{55\magentabox} + x_{55\brickbox} + x_{55\brownbox} = 1 x 55 ■ + x 55 ■ + x 55 ■ + x 55 ■ + x 55 ■ + x 55 ■ + x 55 ■ + x 55 ■ + x 55 ■ + x 55 ■ = 1 Square (5,5) x 56 ■ + x 56 ■ + x 56 ■ + x 56 ■ + x 56 ■ + x 56 ■ + x 56 ■ + x 56 ■ + x 56 ■ + x 56 ■ = 1 x_{56\yellowbox} + x_{56\tealbox} + x_{56\purplebox} + x_{56\greenbox} + x_{56\orangebox} + x_{56\redbox} + x_{56\bluebox} + x_{56\magentabox} + x_{56\brickbox} + x_{56\brownbox} = 1 x 56 ■ + x 56 ■ + x 56 ■ + x 56 ■ + x 56 ■ + x 56 ■ + x 56 ■ + x 56 ■ + x 56 ■ + x 56 ■ = 1 Square (5,6) x 61 ■ + x 61 ■ + x 61 ■ + x 61 ■ + x 61 ■ + x 61 ■ + x 61 ■ + x 61 ■ + x 61 ■ + x 61 ■ = 1 x_{61\yellowbox} + x_{61\tealbox} + x_{61\purplebox} + x_{61\greenbox} + x_{61\orangebox} + x_{61\redbox} + x_{61\bluebox} + x_{61\magentabox} + x_{61\brickbox} + x_{61\brownbox} = 1 x 61 ■ + x 61 ■ + x 61 ■ + x 61 ■ + x 61 ■ + x 61 ■ + x 61 ■ + x 61 ■ + x 61 ■ + x 61 ■ = 1 Square (6,1) x 62 ■ + x 62 ■ + x 62 ■ + x 62 ■ + x 62 ■ + x 62 ■ + x 62 ■ + x 62 ■ + x 62 ■ + x 62 ■ = 1 x_{62\yellowbox} + x_{62\tealbox} + x_{62\purplebox} + x_{62\greenbox} + x_{62\orangebox} + x_{62\redbox} + x_{62\bluebox} + x_{62\magentabox} + x_{62\brickbox} + x_{62\brownbox} = 1 x 62 ■ + x 62 ■ + x 62 ■ + x 62 ■ + x 62 ■ + x 62 ■ + x 62 ■ + x 62 ■ + x 62 ■ + x 62 ■ = 1 Square (6,2) x 63 ■ + x 63 ■ + x 63 ■ + x 63 ■ + x 63 ■ + x 63 ■ + x 63 ■ + x 63 ■ + x 63 ■ + x 63 ■ = 1 x_{63\yellowbox} + x_{63\tealbox} + x_{63\purplebox} + x_{63\greenbox} + x_{63\orangebox} + x_{63\redbox} + x_{63\bluebox} + x_{63\magentabox} + x_{63\brickbox} + x_{63\brownbox} = 1 x 63 ■ + x 63 ■ + x 63 ■ + x 63 ■ + x 63 ■ + x 63 ■ + x 63 ■ + x 63 ■ + x 63 ■ + x 63 ■ = 1 Square (6,3) x 64 ■ + x 64 ■ + x 64 ■ + x 64 ■ + x 64 ■ + x 64 ■ + x 64 ■ + x 64 ■ + x 64 ■ + x 64 ■ = 1 x_{64\yellowbox} + x_{64\tealbox} + x_{64\purplebox} + x_{64\greenbox} + x_{64\orangebox} + x_{64\redbox} + x_{64\bluebox} + x_{64\magentabox} + x_{64\brickbox} + x_{64\brownbox} = 1 x 64 ■ + x 64 ■ + x 64 ■ + x 64 ■ + x 64 ■ + x 64 ■ + x 64 ■ + x 64 ■ + x 64 ■ + x 64 ■ = 1 Square (6,4) x 65 ■ + x 65 ■ + x 65 ■ + x 65 ■ + x 65 ■ + x 65 ■ + x 65 ■ + x 65 ■ + x 65 ■ + x 65 ■ = 1 x_{65\yellowbox} + x_{65\tealbox} + x_{65\purplebox} + x_{65\greenbox} + x_{65\orangebox} + x_{65\redbox} + x_{65\bluebox} + x_{65\magentabox} + x_{65\brickbox} + x_{65\brownbox} = 1 x 65 ■ + x 65 ■ + x 65 ■ + x 65 ■ + x 65 ■ + x 65 ■ + x 65 ■ + x 65 ■ + x 65 ■ + x 65 ■ = 1 Square (6,5) x 66 ■ + x 66 ■ + x 66 ■ + x 66 ■ + x 66 ■ + x 66 ■ + x 66 ■ + x 66 ■ + x 66 ■ + x 66 ■ = 1 x_{66\yellowbox} + x_{66\tealbox} + x_{66\purplebox} + x_{66\greenbox} + x_{66\orangebox} + x_{66\redbox} + x_{66\bluebox} + x_{66\magentabox} + x_{66\brickbox} + x_{66\brownbox} = 1 x 66 ■ + x 66 ■ + x 66 ■ + x 66 ■ + x 66 ■ + x 66 ■ + x 66 ■ + x 66 ■ + x 66 ■ + x 66 ■ = 1 Square (6,6) Top Row Constraints t ■ ≥ 1 t_{\yellowbox} \ge 1 t ■ ≥ 1 Yellow Patch t ■ ≥ 1 t_{\tealbox} \ge 1 t ■ ≥ 1 Teal Patch t ■ ≥ 1 t_{\purplebox} \ge 1 t ■ ≥ 1 Purple Patch t ■ ≥ 1 t_{\greenbox} \ge 1 t ■ ≥ 1 Green Patch t ■ ≥ 1 t_{\orangebox} \ge 1 t ■ ≥ 1 Orange Patch t ■ ≥ 1 t_{\redbox} \ge 1 t ■ ≥ 1 Red Patch t ■ ≥ 1 t_{\bluebox} \ge 1 t ■ ≥ 1 Blue Patch t ■ ≥ 1 t_{\magentabox} \ge 1 t ■ ≥ 1 Magenta Patch t ■ ≥ 1 t_{\brickbox} \ge 1 t ■ ≥ 1 Brick Patch t ■ ≥ 1 t_{\brownbox} \ge 1 t ■ ≥ 1 Brown Patch Bottom Row Constraints t ■ + h ■ − 1 ≤ 6 t_{\yellowbox} + h_{\yellowbox} - 1 \le 6 t ■ + h ■ − 1 ≤ 6 Yellow Patch t ■ + h ■ − 1 ≤ 6 t_{\tealbox} + h_{\tealbox} - 1 \le 6 t ■ + h ■ − 1 ≤ 6 Teal Patch t ■ + h ■ − 1 ≤ 6 t_{\purplebox} + h_{\purplebox} - 1 \le 6 t ■ + h ■ − 1 ≤ 6 Purple Patch t ■ + h ■ − 1 ≤ 6 t_{\greenbox} + h_{\greenbox} - 1 \le 6 t ■ + h ■ − 1 ≤ 6 Green Patch t ■ + h ■ − 1 ≤ 6 t_{\orangebox} + h_{\orangebox} - 1 \le 6 t ■ + h ■ − 1 ≤ 6 Orange Patch t ■ + h ■ − 1 ≤ 6 t_{\redbox} + h_{\redbox} - 1 \le 6 t ■ + h ■ − 1 ≤ 6 Red Patch t ■ + h ■ − 1 ≤ 6 t_{\bluebox} + h_{\bluebox} - 1 \le 6 t ■ + h ■ − 1 ≤ 6 Blue Patch t ■ + h ■ − 1 ≤ 6 t_{\magentabox} + h_{\magentabox} - 1 \le 6 t ■ + h ■ − 1 ≤ 6 Magenta Patch t ■ + h ■ − 1 ≤ 6 t_{\brickbox} + h_{\brickbox} - 1 \le 6 t ■ + h ■ − 1 ≤ 6 Brick Patch t ■ + h ■ − 1 ≤ 6 t_{\brownbox} + h_{\brownbox} - 1 \le 6 t ■ + h ■ − 1 ≤ 6 Brown Patch Leftmost Column Constraints l ■ ≥ 1 l_{\yellowbox} \ge 1 l ■ ≥ 1 Yellow Patch l ■ ≥ 1 l_{\tealbox} \ge 1 l ■ ≥ 1 Teal Patch l ■ ≥ 1 l_{\purplebox} \ge 1 l ■ ≥ 1 Purple Patch l ■ ≥ 1 l_{\greenbox} \ge 1 l ■ ≥ 1 Green Patch l ■ ≥ 1 l_{\orangebox} \ge 1 l ■ ≥ 1 Orange Patch l ■ ≥ 1 l_{\redbox} \ge 1 l ■ ≥ 1 Red Patch l ■ ≥ 1 l_{\bluebox} \ge 1 l ■ ≥ 1 Blue Patch l ■ ≥ 1 l_{\magentabox} \ge 1 l ■ ≥ 1 Magenta Patch l ■ ≥ 1 l_{\brickbox} \ge 1 l ■ ≥ 1 Brick Patch l ■ ≥ 1 l_{\brownbox} \ge 1 l ■ ≥ 1 Brown Patch Rightmost Column Constraints l ■ + w ■ − 1 ≤ 6 l_{\yellowbox} + w_{\yellowbox} - 1 \le 6 l ■ + w ■ − 1 ≤ 6 Yellow Patch l ■ + w ■ − 1 ≤ 6 l_{\tealbox} + w_{\tealbox} - 1 \le 6 l ■ + w ■ − 1 ≤ 6 Teal Patch l ■ + w ■ − 1 ≤ 6 l_{\purplebox} + w_{\purplebox} - 1 \le 6 l ■ + w ■ − 1 ≤ 6 Purple Patch l ■ + w ■ − 1 ≤ 6 l_{\greenbox} + w_{\greenbox} - 1 \le 6 l ■ + w ■ − 1 ≤ 6 Green Patch l ■ + w ■ − 1 ≤ 6 l_{\orangebox} + w_{\orangebox} - 1 \le 6 l ■ + w ■ − 1 ≤ 6 Orange Patch l ■ + w ■ − 1 ≤ 6 l_{\redbox} + w_{\redbox} - 1 \le 6 l ■ + w ■ − 1 ≤ 6 Red Patch l ■ + w ■ − 1 ≤ 6 l_{\bluebox} + w_{\bluebox} - 1 \le 6 l ■ + w ■ − 1 ≤ 6 Blue Patch l ■ + w ■ − 1 ≤ 6 l_{\magentabox} + w_{\magentabox} - 1 \le 6 l ■ + w ■ − 1 ≤ 6 Magenta Patch l ■ + w ■ − 1 ≤ 6 l_{\brickbox} + w_{\brickbox} - 1 \le 6 l ■ + w ■ − 1 ≤ 6 Brick Patch l ■ + w ■ − 1 ≤ 6 l_{\brownbox} + w_{\brownbox} - 1 \le 6 l ■ + w ■ − 1 ≤ 6 Brown Patch Top Boundary Constraints t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) t_{\yellowbox} - 1 \le 6(1-u_{1\yellowbox}) t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) Row 1, Yellow Patch t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) t_{\yellowbox} - 2 \le 6(1-u_{2\yellowbox}) t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) Row 2, Yellow Patch t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) t_{\yellowbox} - 3 \le 6(1-u_{3\yellowbox}) t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) Row 3, Yellow Patch t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) t_{\yellowbox} - 4 \le 6(1-u_{4\yellowbox}) t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) Row 4, Yellow Patch t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) t_{\yellowbox} - 5 \le 6(1-u_{5\yellowbox}) t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) Row 5, Yellow Patch t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) t_{\yellowbox} - 6 \le 6(1-u_{6\yellowbox}) t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) Row 6, Yellow Patch t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) t_{\tealbox} - 1 \le 6(1-u_{1\tealbox}) t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) Row 1, Tealbox Patch t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) t_{\tealbox} - 2 \le 6(1-u_{2\tealbox}) t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) Row 2, Tealbox Patch t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) t_{\tealbox} - 3 \le 6(1-u_{3\tealbox}) t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) Row 3, Tealbox Patch t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) t_{\tealbox} - 4 \le 6(1-u_{4\tealbox}) t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) Row 4, Tealbox Patch t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) t_{\tealbox} - 5 \le 6(1-u_{5\tealbox}) t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) Row 5, Tealbox Patch t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) t_{\tealbox} - 6 \le 6(1-u_{6\tealbox}) t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) Row 6, Tealbox Patch t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) t_{\purplebox} - 1 \le 6(1-u_{1\purplebox}) t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) Row 1, Purple Patch t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) t_{\purplebox} - 2 \le 6(1-u_{2\purplebox}) t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) Row 2, Purple Patch t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) t_{\purplebox} - 3 \le 6(1-u_{3\purplebox}) t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) Row 3, Purple Patch t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) t_{\purplebox} - 4 \le 6(1-u_{4\purplebox}) t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) Row 4, Purple Patch t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) t_{\purplebox} - 5 \le 6(1-u_{5\purplebox}) t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) Row 5, Purple Patch t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) t_{\purplebox} - 6 \le 6(1-u_{6\purplebox}) t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) Row 6, Purple Patch t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) t_{\greenbox} - 1 \le 6(1-u_{1\greenbox}) t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) Row 1, Green Patch t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) t_{\greenbox} - 2 \le 6(1-u_{2\greenbox}) t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) Row 2, Green Patch t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) t_{\greenbox} - 3 \le 6(1-u_{3\greenbox}) t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) Row 3, Green Patch t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) t_{\greenbox} - 4 \le 6(1-u_{4\greenbox}) t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) Row 4, Green Patch t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) t_{\greenbox} - 5 \le 6(1-u_{5\greenbox}) t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) Row 5, Green Patch t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) t_{\greenbox} - 6 \le 6(1-u_{6\greenbox}) t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) Row 6, Green Patch t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) t_{\orangebox} - 1 \le 6(1-u_{1\orangebox}) t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) Row 1, Orange Patch t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) t_{\orangebox} - 2 \le 6(1-u_{2\orangebox}) t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) Row 2, Orange Patch t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) t_{\orangebox} - 3 \le 6(1-u_{3\orangebox}) t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) Row 3, Orange Patch t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) t_{\orangebox} - 4 \le 6(1-u_{4\orangebox}) t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) Row 4, Orange Patch t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) t_{\orangebox} - 5 \le 6(1-u_{5\orangebox}) t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) Row 5, Orange Patch t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) t_{\orangebox} - 6 \le 6(1-u_{6\orangebox}) t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) Row 6, Orange Patch t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) t_{\redbox} - 1 \le 6(1-u_{1\redbox}) t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) Row 1, Red Patch t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) t_{\redbox} - 2 \le 6(1-u_{2\redbox}) t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) Row 2, Red Patch t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) t_{\redbox} - 3 \le 6(1-u_{3\redbox}) t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) Row 3, Red Patch t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) t_{\redbox} - 4 \le 6(1-u_{4\redbox}) t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) Row 4, Red Patch t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) t_{\redbox} - 5 \le 6(1-u_{5\redbox}) t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) Row 5, Red Patch t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) t_{\redbox} - 6 \le 6(1-u_{6\redbox}) t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) Row 6, Red Patch t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) t_{\bluebox} - 1 \le 6(1-u_{1\bluebox}) t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) Row 1, Blue Patch t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) t_{\bluebox} - 2 \le 6(1-u_{2\bluebox}) t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) Row 2, Blue Patch t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) t_{\bluebox} - 3 \le 6(1-u_{3\bluebox}) t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) Row 3, Blue Patch t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) t_{\bluebox} - 4 \le 6(1-u_{4\bluebox}) t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) Row 4, Blue Patch t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) t_{\bluebox} - 5 \le 6(1-u_{5\bluebox}) t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) Row 5, Blue Patch t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) t_{\bluebox} - 6 \le 6(1-u_{6\bluebox}) t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) Row 6, Blue Patch t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) t_{\magentabox} - 1 \le 6(1-u_{1\magentabox}) t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) Row 1, Magenta Patch t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) t_{\magentabox} - 2 \le 6(1-u_{2\magentabox}) t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) Row 2, Magenta Patch t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) t_{\magentabox} - 3 \le 6(1-u_{3\magentabox}) t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) Row 3, Magenta Patch t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) t_{\magentabox} - 4 \le 6(1-u_{4\magentabox}) t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) Row 4, Magenta Patch t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) t_{\magentabox} - 5 \le 6(1-u_{5\magentabox}) t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) Row 5, Magenta Patch t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) t_{\magentabox} - 6 \le 6(1-u_{6\magentabox}) t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) Row 6, Magenta Patch t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) t_{\brickbox} - 1 \le 6(1-u_{1\brickbox}) t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) Row 1, Brick Patch t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) t_{\brickbox} - 2 \le 6(1-u_{2\brickbox}) t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) Row 2, Brick Patch t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) t_{\brickbox} - 3 \le 6(1-u_{3\brickbox}) t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) Row 3, Brick Patch t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) t_{\brickbox} - 4 \le 6(1-u_{4\brickbox}) t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) Row 4, Brick Patch t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) t_{\brickbox} - 5 \le 6(1-u_{5\brickbox}) t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) Row 5, Brick Patch t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) t_{\brickbox} - 6 \le 6(1-u_{6\brickbox}) t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) Row 6, Brick Patch t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) t_{\brownbox} - 1 \le 6(1-u_{1\brownbox}) t ■ − 1 ≤ 6 ( 1 − u 1 ■ ) Row 1, Brown Patch t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) t_{\brownbox} - 2 \le 6(1-u_{2\brownbox}) t ■ − 2 ≤ 6 ( 1 − u 2 ■ ) Row 2, Brown Patch t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) t_{\brownbox} - 3 \le 6(1-u_{3\brownbox}) t ■ − 3 ≤ 6 ( 1 − u 3 ■ ) Row 3, Brown Patch t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) t_{\brownbox} - 4 \le 6(1-u_{4\brownbox}) t ■ − 4 ≤ 6 ( 1 − u 4 ■ ) Row 4, Brown Patch t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) t_{\brownbox} - 5 \le 6(1-u_{5\brownbox}) t ■ − 5 ≤ 6 ( 1 − u 5 ■ ) Row 5, Brown Patch t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) t_{\brownbox} - 6 \le 6(1-u_{6\brownbox}) t ■ − 6 ≤ 6 ( 1 − u 6 ■ ) Row 6, Brown Patch Bottom Boundary Constraints 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) 1 - (t_{\yellowbox} + h_{\yellowbox} - 1) \le 6(1 - u_{1\yellowbox}) 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) Row 1, Yellow Patch 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) 2 - (t_{\yellowbox} + h_{\yellowbox} - 1) \le 6(1 - u_{2\yellowbox}) 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) Row 2, Yellow Patch 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) 3 - (t_{\yellowbox} + h_{\yellowbox} - 1) \le 6(1 - u_{3\yellowbox}) 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) Row 3, Yellow Patch 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) 4 - (t_{\yellowbox} + h_{\yellowbox} - 1) \le 6(1 - u_{4\yellowbox}) 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) Row 4, Yellow Patch 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) 5 - (t_{\yellowbox} + h_{\yellowbox} - 1) \le 6(1 - u_{5\yellowbox}) 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) Row 5, Yellow Patch 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) 6 - (t_{\yellowbox} + h_{\yellowbox} - 1) \le 6(1 - u_{6\yellowbox}) 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) Row 6, Yellow Patch 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) 1 - (t_{\tealbox} + h_{\tealbox} - 1) \le 6(1 - u_{1\tealbox}) 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) Row 1, Tealbox Patch 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) 2 - (t_{\tealbox} + h_{\tealbox} - 1) \le 6(1 - u_{2\tealbox}) 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) Row 2, Tealbox Patch 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) 3 - (t_{\tealbox} + h_{\tealbox} - 1) \le 6(1 - u_{3\tealbox}) 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) Row 3, Tealbox Patch 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) 4 - (t_{\tealbox} + h_{\tealbox} - 1) \le 6(1 - u_{4\tealbox}) 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) Row 4, Tealbox Patch 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) 5 - (t_{\tealbox} + h_{\tealbox} - 1) \le 6(1 - u_{5\tealbox}) 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) Row 5, Tealbox Patch 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) 6 - (t_{\tealbox} + h_{\tealbox} - 1) \le 6(1 - u_{6\tealbox}) 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) Row 6, Tealbox Patch 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) 1 - (t_{\purplebox} + h_{\purplebox} - 1) \le 6(1 - u_{1\purplebox}) 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) Row 1, Purple Patch 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) 2 - (t_{\purplebox} + h_{\purplebox} - 1) \le 6(1 - u_{2\purplebox}) 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) Row 2, Purple Patch 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) 3 - (t_{\purplebox} + h_{\purplebox} - 1) \le 6(1 - u_{3\purplebox}) 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) Row 3, Purple Patch 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) 4 - (t_{\purplebox} + h_{\purplebox} - 1) \le 6(1 - u_{4\purplebox}) 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) Row 4, Purple Patch 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) 5 - (t_{\purplebox} + h_{\purplebox} - 1) \le 6(1 - u_{5\purplebox}) 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) Row 5, Purple Patch 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) 6 - (t_{\purplebox} + h_{\purplebox} - 1) \le 6(1 - u_{6\purplebox}) 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) Row 6, Purple Patch 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) 1 - (t_{\greenbox} + h_{\greenbox} - 1) \le 6(1 - u_{1\greenbox}) 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) Row 1, Green Patch 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) 2 - (t_{\greenbox} + h_{\greenbox} - 1) \le 6(1 - u_{2\greenbox}) 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) Row 2, Green Patch 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) 3 - (t_{\greenbox} + h_{\greenbox} - 1) \le 6(1 - u_{3\greenbox}) 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) Row 3, Green Patch 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) 4 - (t_{\greenbox} + h_{\greenbox} - 1) \le 6(1 - u_{4\greenbox}) 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) Row 4, Green Patch 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) 5 - (t_{\greenbox} + h_{\greenbox} - 1) \le 6(1 - u_{5\greenbox}) 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) Row 5, Green Patch 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) 6 - (t_{\greenbox} + h_{\greenbox} - 1) \le 6(1 - u_{6\greenbox}) 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) Row 6, Green Patch 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) 1 - (t_{\orangebox} + h_{\orangebox} - 1) \le 6(1 - u_{1\orangebox}) 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) Row 1, Orange Patch 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) 2 - (t_{\orangebox} + h_{\orangebox} - 1) \le 6(1 - u_{2\orangebox}) 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) Row 2, Orange Patch 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) 3 - (t_{\orangebox} + h_{\orangebox} - 1) \le 6(1 - u_{3\orangebox}) 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) Row 3, Orange Patch 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) 4 - (t_{\orangebox} + h_{\orangebox} - 1) \le 6(1 - u_{4\orangebox}) 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) Row 4, Orange Patch 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) 5 - (t_{\orangebox} + h_{\orangebox} - 1) \le 6(1 - u_{5\orangebox}) 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) Row 5, Orange Patch 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) 6 - (t_{\orangebox} + h_{\orangebox} - 1) \le 6(1 - u_{6\orangebox}) 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) Row 6, Orange Patch 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) 1 - (t_{\redbox} + h_{\redbox} - 1) \le 6(1 - u_{1\redbox}) 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) Row 1, Red Patch 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) 2 - (t_{\redbox} + h_{\redbox} - 1) \le 6(1 - u_{2\redbox}) 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) Row 2, Red Patch 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) 3 - (t_{\redbox} + h_{\redbox} - 1) \le 6(1 - u_{3\redbox}) 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) Row 3, Red Patch 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) 4 - (t_{\redbox} + h_{\redbox} - 1) \le 6(1 - u_{4\redbox}) 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) Row 4, Red Patch 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) 5 - (t_{\redbox} + h_{\redbox} - 1) \le 6(1 - u_{5\redbox}) 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) Row 5, Red Patch 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) 6 - (t_{\redbox} + h_{\redbox} - 1) \le 6(1 - u_{6\redbox}) 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) Row 6, Red Patch 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) 1 - (t_{\bluebox} + h_{\bluebox} - 1) \le 6(1 - u_{1\bluebox}) 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) Row 1, Blue Patch 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) 2 - (t_{\bluebox} + h_{\bluebox} - 1) \le 6(1 - u_{2\bluebox}) 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) Row 2, Blue Patch 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) 3 - (t_{\bluebox} + h_{\bluebox} - 1) \le 6(1 - u_{3\bluebox}) 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) Row 3, Blue Patch 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) 4 - (t_{\bluebox} + h_{\bluebox} - 1) \le 6(1 - u_{4\bluebox}) 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) Row 4, Blue Patch 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) 5 - (t_{\bluebox} + h_{\bluebox} - 1) \le 6(1 - u_{5\bluebox}) 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) Row 5, Blue Patch 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) 6 - (t_{\bluebox} + h_{\bluebox} - 1) \le 6(1 - u_{6\bluebox}) 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) Row 6, Blue Patch 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) 1 - (t_{\magentabox} + h_{\magentabox} - 1) \le 6(1 - u_{1\magentabox}) 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) Row 1, Magenta Patch 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) 2 - (t_{\magentabox} + h_{\magentabox} - 1) \le 6(1 - u_{2\magentabox}) 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) Row 2, Magenta Patch 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) 3 - (t_{\magentabox} + h_{\magentabox} - 1) \le 6(1 - u_{3\magentabox}) 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) Row 3, Magenta Patch 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) 4 - (t_{\magentabox} + h_{\magentabox} - 1) \le 6(1 - u_{4\magentabox}) 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) Row 4, Magenta Patch 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) 5 - (t_{\magentabox} + h_{\magentabox} - 1) \le 6(1 - u_{5\magentabox}) 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) Row 5, Magenta Patch 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) 6 - (t_{\magentabox} + h_{\magentabox} - 1) \le 6(1 - u_{6\magentabox}) 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) Row 6, Magenta Patch 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) 1 - (t_{\brickbox} + h_{\brickbox} - 1) \le 6(1 - u_{1\brickbox}) 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) Row 1, Brick Patch 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) 2 - (t_{\brickbox} + h_{\brickbox} - 1) \le 6(1 - u_{2\brickbox}) 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) Row 2, Brick Patch 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) 3 - (t_{\brickbox} + h_{\brickbox} - 1) \le 6(1 - u_{3\brickbox}) 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) Row 3, Brick Patch 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) 4 - (t_{\brickbox} + h_{\brickbox} - 1) \le 6(1 - u_{4\brickbox}) 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) Row 4, Brick Patch 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) 5 - (t_{\brickbox} + h_{\brickbox} - 1) \le 6(1 - u_{5\brickbox}) 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) Row 5, Brick Patch 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) 6 - (t_{\brickbox} + h_{\brickbox} - 1) \le 6(1 - u_{6\brickbox}) 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) Row 6, Brick Patch 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) 1 - (t_{\brownbox} + h_{\brownbox} - 1) \le 6(1 - u_{1\brownbox}) 1 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 1 ■ ) Row 1, Brown Patch 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) 2 - (t_{\brownbox} + h_{\brownbox} - 1) \le 6(1 - u_{2\brownbox}) 2 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 2 ■ ) Row 2, Brown Patch 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) 3 - (t_{\brownbox} + h_{\brownbox} - 1) \le 6(1 - u_{3\brownbox}) 3 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 3 ■ ) Row 3, Brown Patch 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) 4 - (t_{\brownbox} + h_{\brownbox} - 1) \le 6(1 - u_{4\brownbox}) 4 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 4 ■ ) Row 4, Brown Patch 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) 5 - (t_{\brownbox} + h_{\brownbox} - 1) \le 6(1 - u_{5\brownbox}) 5 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 5 ■ ) Row 5, Brown Patch 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) 6 - (t_{\brownbox} + h_{\brownbox} - 1) \le 6(1 - u_{6\brownbox}) 6 − ( t ■ + h ■ − 1 ) ≤ 6 ( 1 − u 6 ■ ) Row 6, Brown Patch Left Boundary Constraints l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) l_{\yellowbox} - 1 \le 6(1 - v_{1\yellowbox}) l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) Column 1, Yellow Patch l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) l_{\yellowbox} - 2 \le 6(1 - v_{2\yellowbox}) l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) Column 2, Yellow Patch l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) l_{\yellowbox} - 3 \le 6(1 - v_{3\yellowbox}) l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) Column 3, Yellow Patch l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) l_{\yellowbox} - 4 \le 6(1 - v_{4\yellowbox}) l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) Column 4, Yellow Patch l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) l_{\yellowbox} - 5 \le 6(1 - v_{5\yellowbox}) l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) Column 5, Yellow Patch l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) l_{\yellowbox} - 6 \le 6(1 - v_{6\yellowbox}) l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) Column 6, Yellow Patch l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) l_{\tealbox} - 1 \le 6(1 - v_{1\tealbox}) l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) Column 1, Tealbox Patch l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) l_{\tealbox} - 2 \le 6(1 - v_{2\tealbox}) l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) Column 2, Tealbox Patch l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) l_{\tealbox} - 3 \le 6(1 - v_{3\tealbox}) l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) Column 3, Tealbox Patch l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) l_{\tealbox} - 4 \le 6(1 - v_{4\tealbox}) l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) Column 4, Tealbox Patch l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) l_{\tealbox} - 5 \le 6(1 - v_{5\tealbox}) l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) Column 5, Tealbox Patch l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) l_{\tealbox} - 6 \le 6(1 - v_{6\tealbox}) l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) Column 6, Tealbox Patch l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) l_{\purplebox} - 1 \le 6(1 - v_{1\purplebox}) l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) Column 1, Purple Patch l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) l_{\purplebox} - 2 \le 6(1 - v_{2\purplebox}) l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) Column 2, Purple Patch l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) l_{\purplebox} - 3 \le 6(1 - v_{3\purplebox}) l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) Column 3, Purple Patch l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) l_{\purplebox} - 4 \le 6(1 - v_{4\purplebox}) l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) Column 4, Purple Patch l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) l_{\purplebox} - 5 \le 6(1 - v_{5\purplebox}) l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) Column 5, Purple Patch l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) l_{\purplebox} - 6 \le 6(1 - v_{6\purplebox}) l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) Column 6, Purple Patch l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) l_{\greenbox} - 1 \le 6(1 - v_{1\greenbox}) l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) Column 1, Green Patch l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) l_{\greenbox} - 2 \le 6(1 - v_{2\greenbox}) l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) Column 2, Green Patch l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) l_{\greenbox} - 3 \le 6(1 - v_{3\greenbox}) l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) Column 3, Green Patch l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) l_{\greenbox} - 4 \le 6(1 - v_{4\greenbox}) l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) Column 4, Green Patch l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) l_{\greenbox} - 5 \le 6(1 - v_{5\greenbox}) l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) Column 5, Green Patch l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) l_{\greenbox} - 6 \le 6(1 - v_{6\greenbox}) l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) Column 6, Green Patch l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) l_{\orangebox} - 1 \le 6(1 - v_{1\orangebox}) l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) Column 1, Orange Patch l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) l_{\orangebox} - 2 \le 6(1 - v_{2\orangebox}) l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) Column 2, Orange Patch l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) l_{\orangebox} - 3 \le 6(1 - v_{3\orangebox}) l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) Column 3, Orange Patch l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) l_{\orangebox} - 4 \le 6(1 - v_{4\orangebox}) l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) Column 4, Orange Patch l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) l_{\orangebox} - 5 \le 6(1 - v_{5\orangebox}) l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) Column 5, Orange Patch l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) l_{\orangebox} - 6 \le 6(1 - v_{6\orangebox}) l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) Column 6, Orange Patch l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) l_{\redbox} - 1 \le 6(1 - v_{1\redbox}) l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) Column 1, Red Patch l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) l_{\redbox} - 2 \le 6(1 - v_{2\redbox}) l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) Column 2, Red Patch l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) l_{\redbox} - 3 \le 6(1 - v_{3\redbox}) l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) Column 3, Red Patch l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) l_{\redbox} - 4 \le 6(1 - v_{4\redbox}) l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) Column 4, Red Patch l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) l_{\redbox} - 5 \le 6(1 - v_{5\redbox}) l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) Column 5, Red Patch l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) l_{\redbox} - 6 \le 6(1 - v_{6\redbox}) l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) Column 6, Red Patch l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) l_{\bluebox} - 1 \le 6(1 - v_{1\bluebox}) l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) Column 1, Blue Patch l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) l_{\bluebox} - 2 \le 6(1 - v_{2\bluebox}) l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) Column 2, Blue Patch l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) l_{\bluebox} - 3 \le 6(1 - v_{3\bluebox}) l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) Column 3, Blue Patch l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) l_{\bluebox} - 4 \le 6(1 - v_{4\bluebox}) l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) Column 4, Blue Patch l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) l_{\bluebox} - 5 \le 6(1 - v_{5\bluebox}) l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) Column 5, Blue Patch l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) l_{\bluebox} - 6 \le 6(1 - v_{6\bluebox}) l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) Column 6, Blue Patch l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) l_{\magentabox} - 1 \le 6(1 - v_{1\magentabox}) l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) Column 1, Magenta Patch l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) l_{\magentabox} - 2 \le 6(1 - v_{2\magentabox}) l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) Column 2, Magenta Patch l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) l_{\magentabox} - 3 \le 6(1 - v_{3\magentabox}) l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) Column 3, Magenta Patch l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) l_{\magentabox} - 4 \le 6(1 - v_{4\magentabox}) l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) Column 4, Magenta Patch l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) l_{\magentabox} - 5 \le 6(1 - v_{5\magentabox}) l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) Column 5, Magenta Patch l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) l_{\magentabox} - 6 \le 6(1 - v_{6\magentabox}) l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) Column 6, Magenta Patch l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) l_{\brickbox} - 1 \le 6(1 - v_{1\brickbox}) l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) Column 1, Brick Patch l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) l_{\brickbox} - 2 \le 6(1 - v_{2\brickbox}) l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) Column 2, Brick Patch l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) l_{\brickbox} - 3 \le 6(1 - v_{3\brickbox}) l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) Column 3, Brick Patch l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) l_{\brickbox} - 4 \le 6(1 - v_{4\brickbox}) l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) Column 4, Brick Patch l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) l_{\brickbox} - 5 \le 6(1 - v_{5\brickbox}) l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) Column 5, Brick Patch l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) l_{\brickbox} - 6 \le 6(1 - v_{6\brickbox}) l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) Column 6, Brick Patch l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) l_{\brownbox} - 1 \le 6(1 - v_{1\brownbox}) l ■ − 1 ≤ 6 ( 1 − v 1 ■ ) Column 1, Brown Patch l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) l_{\brownbox} - 2 \le 6(1 - v_{2\brownbox}) l ■ − 2 ≤ 6 ( 1 − v 2 ■ ) Column 2, Brown Patch l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) l_{\brownbox} - 3 \le 6(1 - v_{3\brownbox}) l ■ − 3 ≤ 6 ( 1 − v 3 ■ ) Column 3, Brown Patch l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) l_{\brownbox} - 4 \le 6(1 - v_{4\brownbox}) l ■ − 4 ≤ 6 ( 1 − v 4 ■ ) Column 4, Brown Patch l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) l_{\brownbox} - 5 \le 6(1 - v_{5\brownbox}) l ■ − 5 ≤ 6 ( 1 − v 5 ■ ) Column 5, Brown Patch l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) l_{\brownbox} - 6 \le 6(1 - v_{6\brownbox}) l ■ − 6 ≤ 6 ( 1 − v 6 ■ ) Column 6, Brown Patch Right Boundary Constraints 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) 1 - (l_{\yellowbox} + w_{\yellowbox} - 1) \le 6(1 - v_{1\yellowbox}) 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) Column 1, Yellow Patch 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) 2 - (l_{\yellowbox} + w_{\yellowbox} - 1) \le 6(1 - v_{2\yellowbox}) 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) Column 2, Yellow Patch 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) 3 - (l_{\yellowbox} + w_{\yellowbox} - 1) \le 6(1 - v_{3\yellowbox}) 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) Column 3, Yellow Patch 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) 4 - (l_{\yellowbox} + w_{\yellowbox} - 1) \le 6(1 - v_{4\yellowbox}) 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) Column 4, Yellow Patch 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) 5 - (l_{\yellowbox} + w_{\yellowbox} - 1) \le 6(1 - v_{5\yellowbox}) 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) Column 5, Yellow Patch 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) 6 - (l_{\yellowbox} + w_{\yellowbox} - 1) \le 6(1 - v_{6\yellowbox}) 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) Column 6, Yellow Patch 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) 1 - (l_{\tealbox} + w_{\tealbox} - 1) \le 6(1 - v_{1\tealbox}) 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) Column 1, Tealbox Patch 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) 2 - (l_{\tealbox} + w_{\tealbox} - 1) \le 6(1 - v_{2\tealbox}) 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) Column 2, Tealbox Patch 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) 3 - (l_{\tealbox} + w_{\tealbox} - 1) \le 6(1 - v_{3\tealbox}) 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) Column 3, Tealbox Patch 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) 4 - (l_{\tealbox} + w_{\tealbox} - 1) \le 6(1 - v_{4\tealbox}) 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) Column 4, Tealbox Patch 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) 5 - (l_{\tealbox} + w_{\tealbox} - 1) \le 6(1 - v_{5\tealbox}) 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) Column 5, Tealbox Patch 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) 6 - (l_{\tealbox} + w_{\tealbox} - 1) \le 6(1 - v_{6\tealbox}) 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) Column 6, Tealbox Patch 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) 1 - (l_{\purplebox} + w_{\purplebox} - 1) \le 6(1 - v_{1\purplebox}) 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) Column 1, Purple Patch 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) 2 - (l_{\purplebox} + w_{\purplebox} - 1) \le 6(1 - v_{2\purplebox}) 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) Column 2, Purple Patch 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) 3 - (l_{\purplebox} + w_{\purplebox} - 1) \le 6(1 - v_{3\purplebox}) 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) Column 3, Purple Patch 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) 4 - (l_{\purplebox} + w_{\purplebox} - 1) \le 6(1 - v_{4\purplebox}) 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) Column 4, Purple Patch 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) 5 - (l_{\purplebox} + w_{\purplebox} - 1) \le 6(1 - v_{5\purplebox}) 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) Column 5, Purple Patch 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) 6 - (l_{\purplebox} + w_{\purplebox} - 1) \le 6(1 - v_{6\purplebox}) 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) Column 6, Purple Patch 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) 1 - (l_{\greenbox} + w_{\greenbox} - 1) \le 6(1 - v_{1\greenbox}) 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) Column 1, Green Patch 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) 2 - (l_{\greenbox} + w_{\greenbox} - 1) \le 6(1 - v_{2\greenbox}) 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) Column 2, Green Patch 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) 3 - (l_{\greenbox} + w_{\greenbox} - 1) \le 6(1 - v_{3\greenbox}) 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) Column 3, Green Patch 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) 4 - (l_{\greenbox} + w_{\greenbox} - 1) \le 6(1 - v_{4\greenbox}) 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) Column 4, Green Patch 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) 5 - (l_{\greenbox} + w_{\greenbox} - 1) \le 6(1 - v_{5\greenbox}) 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) Column 5, Green Patch 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) 6 - (l_{\greenbox} + w_{\greenbox} - 1) \le 6(1 - v_{6\greenbox}) 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) Column 6, Green Patch 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) 1 - (l_{\orangebox} + w_{\orangebox} - 1) \le 6(1 - v_{1\orangebox}) 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) Column 1, Orange Patch 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) 2 - (l_{\orangebox} + w_{\orangebox} - 1) \le 6(1 - v_{2\orangebox}) 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) Column 2, Orange Patch 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) 3 - (l_{\orangebox} + w_{\orangebox} - 1) \le 6(1 - v_{3\orangebox}) 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) Column 3, Orange Patch 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) 4 - (l_{\orangebox} + w_{\orangebox} - 1) \le 6(1 - v_{4\orangebox}) 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) Column 4, Orange Patch 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) 5 - (l_{\orangebox} + w_{\orangebox} - 1) \le 6(1 - v_{5\orangebox}) 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) Column 5, Orange Patch 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) 6 - (l_{\orangebox} + w_{\orangebox} - 1) \le 6(1 - v_{6\orangebox}) 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) Column 6, Orange Patch 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) 1 - (l_{\redbox} + w_{\redbox} - 1) \le 6(1 - v_{1\redbox}) 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) Column 1, Red Patch 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) 2 - (l_{\redbox} + w_{\redbox} - 1) \le 6(1 - v_{2\redbox}) 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) Column 2, Red Patch 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) 3 - (l_{\redbox} + w_{\redbox} - 1) \le 6(1 - v_{3\redbox}) 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) Column 3, Red Patch 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) 4 - (l_{\redbox} + w_{\redbox} - 1) \le 6(1 - v_{4\redbox}) 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) Column 4, Red Patch 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) 5 - (l_{\redbox} + w_{\redbox} - 1) \le 6(1 - v_{5\redbox}) 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) Column 5, Red Patch 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) 6 - (l_{\redbox} + w_{\redbox} - 1) \le 6(1 - v_{6\redbox}) 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) Column 6, Red Patch 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) 1 - (l_{\bluebox} + w_{\bluebox} - 1) \le 6(1 - v_{1\bluebox}) 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) Column 1, Blue Patch 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) 2 - (l_{\bluebox} + w_{\bluebox} - 1) \le 6(1 - v_{2\bluebox}) 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) Column 2, Blue Patch 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) 3 - (l_{\bluebox} + w_{\bluebox} - 1) \le 6(1 - v_{3\bluebox}) 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) Column 3, Blue Patch 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) 4 - (l_{\bluebox} + w_{\bluebox} - 1) \le 6(1 - v_{4\bluebox}) 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) Column 4, Blue Patch 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) 5 - (l_{\bluebox} + w_{\bluebox} - 1) \le 6(1 - v_{5\bluebox}) 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) Column 5, Blue Patch 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) 6 - (l_{\bluebox} + w_{\bluebox} - 1) \le 6(1 - v_{6\bluebox}) 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) Column 6, Blue Patch 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) 1 - (l_{\magentabox} + w_{\magentabox} - 1) \le 6(1 - v_{1\magentabox}) 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) Column 1, Magenta Patch 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) 2 - (l_{\magentabox} + w_{\magentabox} - 1) \le 6(1 - v_{2\magentabox}) 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) Column 2, Magenta Patch 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) 3 - (l_{\magentabox} + w_{\magentabox} - 1) \le 6(1 - v_{3\magentabox}) 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) Column 3, Magenta Patch 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) 4 - (l_{\magentabox} + w_{\magentabox} - 1) \le 6(1 - v_{4\magentabox}) 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) Column 4, Magenta Patch 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) 5 - (l_{\magentabox} + w_{\magentabox} - 1) \le 6(1 - v_{5\magentabox}) 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) Column 5, Magenta Patch 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) 6 - (l_{\magentabox} + w_{\magentabox} - 1) \le 6(1 - v_{6\magentabox}) 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) Column 6, Magenta Patch 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) 1 - (l_{\brickbox} + w_{\brickbox} - 1) \le 6(1 - v_{1\brickbox}) 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) Column 1, Brick Patch 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) 2 - (l_{\brickbox} + w_{\brickbox} - 1) \le 6(1 - v_{2\brickbox}) 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) Column 2, Brick Patch 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) 3 - (l_{\brickbox} + w_{\brickbox} - 1) \le 6(1 - v_{3\brickbox}) 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) Column 3, Brick Patch 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) 4 - (l_{\brickbox} + w_{\brickbox} - 1) \le 6(1 - v_{4\brickbox}) 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) Column 4, Brick Patch 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) 5 - (l_{\brickbox} + w_{\brickbox} - 1) \le 6(1 - v_{5\brickbox}) 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) Column 5, Brick Patch 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) 6 - (l_{\brickbox} + w_{\brickbox} - 1) \le 6(1 - v_{6\brickbox}) 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) Column 6, Brick Patch 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) 1 - (l_{\brownbox} + w_{\brownbox} - 1) \le 6(1 - v_{1\brownbox}) 1 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 1 ■ ) Column 1, Brown Patch 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) 2 - (l_{\brownbox} + w_{\brownbox} - 1) \le 6(1 - v_{2\brownbox}) 2 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 2 ■ ) Column 2, Brown Patch 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) 3 - (l_{\brownbox} + w_{\brownbox} - 1) \le 6(1 - v_{3\brownbox}) 3 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 3 ■ ) Column 3, Brown Patch 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) 4 - (l_{\brownbox} + w_{\brownbox} - 1) \le 6(1 - v_{4\brownbox}) 4 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 4 ■ ) Column 4, Brown Patch 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) 5 - (l_{\brownbox} + w_{\brownbox} - 1) \le 6(1 - v_{5\brownbox}) 5 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 5 ■ ) Column 5, Brown Patch 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) 6 - (l_{\brownbox} + w_{\brownbox} - 1) \le 6(1 - v_{6\brownbox}) 6 − ( l ■ + w ■ − 1 ) ≤ 6 ( 1 − v 6 ■ ) Column 6, Brown Patch Height Constraints u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ u_{1\yellowbox} + u_{2\yellowbox} + u_{3\yellowbox} + u_{4\yellowbox} + u_{5\yellowbox} + u_{6\yellowbox} = h_{\yellowbox} u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ Yellow Patch_ u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ u_{1\tealbox} + u_{2\tealbox} + u_{3\tealbox} + u_{4\tealbox} + u_{5\tealbox} + u_{6\tealbox} = h_{\tealbox} u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ Teal Patch_ u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ u_{1\purplebox} + u_{2\purplebox} + u_{3\purplebox} + u_{4\purplebox} + u_{5\purplebox} + u_{6\purplebox} = h_{\purplebox} u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ Purple Patch_ u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ u_{1\greenbox} + u_{2\greenbox} + u_{3\greenbox} + u_{4\greenbox} + u_{5\greenbox} + u_{6\greenbox} = h_{\greenbox} u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ Green Patch_ u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ u_{1\orangebox} + u_{2\orangebox} + u_{3\orangebox} + u_{4\orangebox} + u_{5\orangebox} + u_{6\orangebox} = h_{\orangebox} u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ Orange Patch_ u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ u_{1\redbox} + u_{2\redbox} + u_{3\redbox} + u_{4\redbox} + u_{5\redbox} + u_{6\redbox} = h_{\redbox} u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ Red Patch_ u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ u_{1\bluebox} + u_{2\bluebox} + u_{3\bluebox} + u_{4\bluebox} + u_{5\bluebox} + u_{6\bluebox} = h_{\bluebox} u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ Blue Patch_ u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ u_{1\magentabox} + u_{2\magentabox} + u_{3\magentabox} + u_{4\magentabox} + u_{5\magentabox} + u_{6\magentabox} = h_{\magentabox} u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ Magenta Patch_ u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ u_{1\brickbox} + u_{2\brickbox} + u_{3\brickbox} + u_{4\brickbox} + u_{5\brickbox} + u_{6\brickbox} = h_{\brickbox} u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ Brick Patch_ u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ u_{1\brownbox} + u_{2\brownbox} + u_{3\brownbox} + u_{4\brownbox} + u_{5\brownbox} + u_{6\brownbox} = h_{\brownbox} u 1 ■ + u 2 ■ + u 3 ■ + u 4 ■ + u 5 ■ + u 6 ■ = h ■ Brown Patch_ Width Constraints v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ v_{1\yellowbox} + v_{2\yellowbox} + v_{3\yellowbox} + v_{4\yellowbox} + v_{5\yellowbox} + v_{6\yellowbox} = w_{\yellowbox} v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ Yellow Patch_ v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ v_{1\tealbox} + v_{2\tealbox} + v_{3\tealbox} + v_{4\tealbox} + v_{5\tealbox} + v_{6\tealbox} = w_{\tealbox} v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ Teal Patch_ v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ v_{1\purplebox} + v_{2\purplebox} + v_{3\purplebox} + v_{4\purplebox} + v_{5\purplebox} + v_{6\purplebox} = w_{\purplebox} v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ Purple Patch_ v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ v_{1\greenbox} + v_{2\greenbox} + v_{3\greenbox} + v_{4\greenbox} + v_{5\greenbox} + v_{6\greenbox} = w_{\greenbox} v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ Green Patch_ v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ v_{1\orangebox} + v_{2\orangebox} + v_{3\orangebox} + v_{4\orangebox} + v_{5\orangebox} + v_{6\orangebox} = w_{\orangebox} v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ Orange Patch_ v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ v_{1\redbox} + v_{2\redbox} + v_{3\redbox} + v_{4\redbox} + v_{5\redbox} + v_{6\redbox} = w_{\redbox} v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ Red Patch_ v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ v_{1\bluebox} + v_{2\bluebox} + v_{3\bluebox} + v_{4\bluebox} + v_{5\bluebox} + v_{6\bluebox} = w_{\bluebox} v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ Blue Patch_ v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ v_{1\magentabox} + v_{2\magentabox} + v_{3\magentabox} + v_{4\magentabox} + v_{5\magentabox} + v_{6\magentabox} = w_{\magentabox} v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ Magenta Patch_ v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ v_{1\brickbox} + v_{2\brickbox} + v_{3\brickbox} + v_{4\brickbox} + v_{5\brickbox} + v_{6\brickbox} = w_{\brickbox} v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ Brick Patch_ v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ v_{1\brownbox} + v_{2\brownbox} + v_{3\brownbox} + v_{4\brownbox} + v_{5\brownbox} + v_{6\brownbox} = w_{\brownbox} v 1 ■ + v 2 ■ + v 3 ■ + v 4 ■ + v 5 ■ + v 6 ■ = w ■ Brown Patch_ Cutout-Rows Constraints x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ x_{11\yellowbox} + x_{12\yellowbox} + x_{13\yellowbox} + x_{14\yellowbox} + x_{15\yellowbox} + x_{16\yellowbox} \le 6u_{1\yellowbox} x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ Row 1, Yellow Patch x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ x_{21\yellowbox} + x_{22\yellowbox} + x_{23\yellowbox} + x_{24\yellowbox} + x_{25\yellowbox} + x_{26\yellowbox} \le 6u_{2\yellowbox} x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ Row 2, Yellow Patch x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ x_{31\yellowbox} + x_{32\yellowbox} + x_{33\yellowbox} + x_{34\yellowbox} + x_{35\yellowbox} + x_{36\yellowbox} \le 6u_{3\yellowbox} x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ Row 3, Yellow Patch x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ x_{41\yellowbox} + x_{42\yellowbox} + x_{43\yellowbox} + x_{44\yellowbox} + x_{45\yellowbox} + x_{46\yellowbox} \le 6u_{4\yellowbox} x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ Row 4, Yellow Patch x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ x_{51\yellowbox} + x_{52\yellowbox} + x_{53\yellowbox} + x_{54\yellowbox} + x_{55\yellowbox} + x_{56\yellowbox} \le 6u_{5\yellowbox} x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ Row 5, Yellow Patch x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ x_{61\yellowbox} + x_{62\yellowbox} + x_{63\yellowbox} + x_{64\yellowbox} + x_{65\yellowbox} + x_{66\yellowbox} \le 6u_{6\yellowbox} x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ Row 6, Yellow Patch x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ x_{11\tealbox} + x_{12\tealbox} + x_{13\tealbox} + x_{14\tealbox} + x_{15\tealbox} + x_{16\tealbox} \le 6u_{1\tealbox} x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ Row 1, Teal x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ x_{21\tealbox} + x_{22\tealbox} + x_{23\tealbox} + x_{24\tealbox} + x_{25\tealbox} + x_{26\tealbox} \le 6u_{2\tealbox} x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ Row 2, Teal x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ x_{31\tealbox} + x_{32\tealbox} + x_{33\tealbox} + x_{34\tealbox} + x_{35\tealbox} + x_{36\tealbox} \le 6u_{3\tealbox} x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ Row 3, Teal x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ x_{41\tealbox} + x_{42\tealbox} + x_{43\tealbox} + x_{44\tealbox} + x_{45\tealbox} + x_{46\tealbox} \le 6u_{4\tealbox} x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ Row 4, Teal x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ x_{51\tealbox} + x_{52\tealbox} + x_{53\tealbox} + x_{54\tealbox} + x_{55\tealbox} + x_{56\tealbox} \le 6u_{5\tealbox} x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ Row 5, Teal x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ x_{61\tealbox} + x_{62\tealbox} + x_{63\tealbox} + x_{64\tealbox} + x_{65\tealbox} + x_{66\tealbox} \le 6u_{6\tealbox} x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ Row 6, Teal x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ x_{11\purplebox} + x_{12\purplebox} + x_{13\purplebox} + x_{14\purplebox} + x_{15\purplebox} + x_{16\purplebox} \le 6u_{1\purplebox} x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ Row 1, Purple Patch x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ x_{21\purplebox} + x_{22\purplebox} + x_{23\purplebox} + x_{24\purplebox} + x_{25\purplebox} + x_{26\purplebox} \le 6u_{2\purplebox} x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ Row 2, Purple Patch x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ x_{31\purplebox} + x_{32\purplebox} + x_{33\purplebox} + x_{34\purplebox} + x_{35\purplebox} + x_{36\purplebox} \le 6u_{3\purplebox} x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ Row 3, Purple Patch x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ x_{41\purplebox} + x_{42\purplebox} + x_{43\purplebox} + x_{44\purplebox} + x_{45\purplebox} + x_{46\purplebox} \le 6u_{4\purplebox} x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ Row 4, Purple Patch x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ x_{51\purplebox} + x_{52\purplebox} + x_{53\purplebox} + x_{54\purplebox} + x_{55\purplebox} + x_{56\purplebox} \le 6u_{5\purplebox} x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ Row 5, Purple Patch x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ x_{61\purplebox} + x_{62\purplebox} + x_{63\purplebox} + x_{64\purplebox} + x_{65\purplebox} + x_{66\purplebox} \le 6u_{6\purplebox} x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ Row 6, Purple Patch x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ x_{11\greenbox} + x_{12\greenbox} + x_{13\greenbox} + x_{14\greenbox} + x_{15\greenbox} + x_{16\greenbox} \le 6u_{1\greenbox} x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ Row 1, Green Patch x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ x_{21\greenbox} + x_{22\greenbox} + x_{23\greenbox} + x_{24\greenbox} + x_{25\greenbox} + x_{26\greenbox} \le 6u_{2\greenbox} x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ Row 2, Green Patch x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ x_{31\greenbox} + x_{32\greenbox} + x_{33\greenbox} + x_{34\greenbox} + x_{35\greenbox} + x_{36\greenbox} \le 6u_{3\greenbox} x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ Row 3, Green Patch x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ x_{41\greenbox} + x_{42\greenbox} + x_{43\greenbox} + x_{44\greenbox} + x_{45\greenbox} + x_{46\greenbox} \le 6u_{4\greenbox} x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ Row 4, Green Patch x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ x_{51\greenbox} + x_{52\greenbox} + x_{53\greenbox} + x_{54\greenbox} + x_{55\greenbox} + x_{56\greenbox} \le 6u_{5\greenbox} x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ Row 5, Green Patch x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ x_{61\greenbox} + x_{62\greenbox} + x_{63\greenbox} + x_{64\greenbox} + x_{65\greenbox} + x_{66\greenbox} \le 6u_{6\greenbox} x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ Row 6, Green Patch x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ x_{11\orangebox} + x_{12\orangebox} + x_{13\orangebox} + x_{14\orangebox} + x_{15\orangebox} + x_{16\orangebox} \le 6u_{1\orangebox} x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ Row 1, Orange Patch x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ x_{21\orangebox} + x_{22\orangebox} + x_{23\orangebox} + x_{24\orangebox} + x_{25\orangebox} + x_{26\orangebox} \le 6u_{2\orangebox} x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ Row 2, Orange Patch x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ x_{31\orangebox} + x_{32\orangebox} + x_{33\orangebox} + x_{34\orangebox} + x_{35\orangebox} + x_{36\orangebox} \le 6u_{3\orangebox} x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ Row 3, Orange Patch x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ x_{41\orangebox} + x_{42\orangebox} + x_{43\orangebox} + x_{44\orangebox} + x_{45\orangebox} + x_{46\orangebox} \le 6u_{4\orangebox} x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ Row 4, Orange Patch x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ x_{51\orangebox} + x_{52\orangebox} + x_{53\orangebox} + x_{54\orangebox} + x_{55\orangebox} + x_{56\orangebox} \le 6u_{5\orangebox} x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ Row 5, Orange Patch x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ x_{61\orangebox} + x_{62\orangebox} + x_{63\orangebox} + x_{64\orangebox} + x_{65\orangebox} + x_{66\orangebox} \le 6u_{6\orangebox} x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ Row 6, Orange Patch x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ x_{11\redbox} + x_{12\redbox} + x_{13\redbox} + x_{14\redbox} + x_{15\redbox} + x_{16\redbox} \le 6u_{1\redbox} x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ Row 1, Red Patch x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ x_{21\redbox} + x_{22\redbox} + x_{23\redbox} + x_{24\redbox} + x_{25\redbox} + x_{26\redbox} \le 6u_{2\redbox} x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ Row 2, Red Patch x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ x_{31\redbox} + x_{32\redbox} + x_{33\redbox} + x_{34\redbox} + x_{35\redbox} + x_{36\redbox} \le 6u_{3\redbox} x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ Row 3, Red Patch x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ x_{41\redbox} + x_{42\redbox} + x_{43\redbox} + x_{44\redbox} + x_{45\redbox} + x_{46\redbox} \le 6u_{4\redbox} x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ Row 4, Red Patch x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ x_{51\redbox} + x_{52\redbox} + x_{53\redbox} + x_{54\redbox} + x_{55\redbox} + x_{56\redbox} \le 6u_{5\redbox} x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ Row 5, Red Patch x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ x_{61\redbox} + x_{62\redbox} + x_{63\redbox} + x_{64\redbox} + x_{65\redbox} + x_{66\redbox} \le 6u_{6\redbox} x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ Row 6, Red Patch x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ x_{11\bluebox} + x_{12\bluebox} + x_{13\bluebox} + x_{14\bluebox} + x_{15\bluebox} + x_{16\bluebox} \le 6u_{1\bluebox} x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ Row 1, Blue Patch x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ x_{21\bluebox} + x_{22\bluebox} + x_{23\bluebox} + x_{24\bluebox} + x_{25\bluebox} + x_{26\bluebox} \le 6u_{2\bluebox} x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ Row 2, Blue Patch x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ x_{31\bluebox} + x_{32\bluebox} + x_{33\bluebox} + x_{34\bluebox} + x_{35\bluebox} + x_{36\bluebox} \le 6u_{3\bluebox} x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ Row 3, Blue Patch x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ x_{41\bluebox} + x_{42\bluebox} + x_{43\bluebox} + x_{44\bluebox} + x_{45\bluebox} + x_{46\bluebox} \le 6u_{4\bluebox} x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ Row 4, Blue Patch x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ x_{51\bluebox} + x_{52\bluebox} + x_{53\bluebox} + x_{54\bluebox} + x_{55\bluebox} + x_{56\bluebox} \le 6u_{5\bluebox} x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ Row 5, Blue Patch x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ x_{61\bluebox} + x_{62\bluebox} + x_{63\bluebox} + x_{64\bluebox} + x_{65\bluebox} + x_{66\bluebox} \le 6u_{6\bluebox} x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ Row 6, Blue Patch x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ x_{11\magentabox} + x_{12\magentabox} + x_{13\magentabox} + x_{14\magentabox} + x_{15\magentabox} + x_{16\magentabox} \le 6u_{1\magentabox} x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ Row 1, Magenta Patch x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ x_{21\magentabox} + x_{22\magentabox} + x_{23\magentabox} + x_{24\magentabox} + x_{25\magentabox} + x_{26\magentabox} \le 6u_{2\magentabox} x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ Row 2, Magenta Patch x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ x_{31\magentabox} + x_{32\magentabox} + x_{33\magentabox} + x_{34\magentabox} + x_{35\magentabox} + x_{36\magentabox} \le 6u_{3\magentabox} x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ Row 3, Magenta Patch x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ x_{41\magentabox} + x_{42\magentabox} + x_{43\magentabox} + x_{44\magentabox} + x_{45\magentabox} + x_{46\magentabox} \le 6u_{4\magentabox} x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ Row 4, Magenta Patch x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ x_{51\magentabox} + x_{52\magentabox} + x_{53\magentabox} + x_{54\magentabox} + x_{55\magentabox} + x_{56\magentabox} \le 6u_{5\magentabox} x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ Row 5, Magenta Patch x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ x_{61\magentabox} + x_{62\magentabox} + x_{63\magentabox} + x_{64\magentabox} + x_{65\magentabox} + x_{66\magentabox} \le 6u_{6\magentabox} x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ Row 6, Magenta Patch x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ x_{11\brickbox} + x_{12\brickbox} + x_{13\brickbox} + x_{14\brickbox} + x_{15\brickbox} + x_{16\brickbox} \le 6u_{1\brickbox} x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ Row 1, Brick Patch x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ x_{21\brickbox} + x_{22\brickbox} + x_{23\brickbox} + x_{24\brickbox} + x_{25\brickbox} + x_{26\brickbox} \le 6u_{2\brickbox} x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ Row 2, Brick Patch x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ x_{31\brickbox} + x_{32\brickbox} + x_{33\brickbox} + x_{34\brickbox} + x_{35\brickbox} + x_{36\brickbox} \le 6u_{3\brickbox} x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ Row 3, Brick Patch x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ x_{41\brickbox} + x_{42\brickbox} + x_{43\brickbox} + x_{44\brickbox} + x_{45\brickbox} + x_{46\brickbox} \le 6u_{4\brickbox} x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ Row 4, Brick Patch x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ x_{51\brickbox} + x_{52\brickbox} + x_{53\brickbox} + x_{54\brickbox} + x_{55\brickbox} + x_{56\brickbox} \le 6u_{5\brickbox} x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ Row 5, Brick Patch x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ x_{61\brickbox} + x_{62\brickbox} + x_{63\brickbox} + x_{64\brickbox} + x_{65\brickbox} + x_{66\brickbox} \le 6u_{6\brickbox} x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ Row 6, Brick Patch x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ x_{11\brownbox} + x_{12\brownbox} + x_{13\brownbox} + x_{14\brownbox} + x_{15\brownbox} + x_{16\brownbox} \le 6u_{1\brownbox} x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ ≤ 6 u 1 ■ Row 1, Brown Patch x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ x_{21\brownbox} + x_{22\brownbox} + x_{23\brownbox} + x_{24\brownbox} + x_{25\brownbox} + x_{26\brownbox} \le 6u_{2\brownbox} x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ ≤ 6 u 2 ■ Row 2, Brown Patch x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ x_{31\brownbox} + x_{32\brownbox} + x_{33\brownbox} + x_{34\brownbox} + x_{35\brownbox} + x_{36\brownbox} \le 6u_{3\brownbox} x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ ≤ 6 u 3 ■ Row 3, Brown Patch x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ x_{41\brownbox} + x_{42\brownbox} + x_{43\brownbox} + x_{44\brownbox} + x_{45\brownbox} + x_{46\brownbox} \le 6u_{4\brownbox} x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ ≤ 6 u 4 ■ Row 4, Brown Patch x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ x_{51\brownbox} + x_{52\brownbox} + x_{53\brownbox} + x_{54\brownbox} + x_{55\brownbox} + x_{56\brownbox} \le 6u_{5\brownbox} x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ ≤ 6 u 5 ■ Row 5, Brown Patch x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ x_{61\brownbox} + x_{62\brownbox} + x_{63\brownbox} + x_{64\brownbox} + x_{65\brownbox} + x_{66\brownbox} \le 6u_{6\brownbox} x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ ≤ 6 u 6 ■ Row 6, Brown Patch Cutout-Columns Constraints x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ x_{11\yellowbox} + x_{21\yellowbox} + x_{31\yellowbox} + x_{41\yellowbox} + x_{51\yellowbox} + x_{61\yellowbox} \le 6v_{1\yellowbox} x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ Column 1, Yellow Patch x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ x_{12\yellowbox} + x_{22\yellowbox} + x_{32\yellowbox} + x_{42\yellowbox} + x_{52\yellowbox} + x_{62\yellowbox} \le 6v_{2\yellowbox} x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ Column 2, Yellow Patch x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ x_{13\yellowbox} + x_{23\yellowbox} + x_{33\yellowbox} + x_{43\yellowbox} + x_{53\yellowbox} + x_{63\yellowbox} \le 6v_{3\yellowbox} x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ Column 3, Yellow Patch x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ x_{14\yellowbox} + x_{24\yellowbox} + x_{34\yellowbox} + x_{44\yellowbox} + x_{54\yellowbox} + x_{64\yellowbox} \le 6v_{4\yellowbox} x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ Column 4, Yellow Patch x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ x_{15\yellowbox} + x_{25\yellowbox} + x_{35\yellowbox} + x_{45\yellowbox} + x_{55\yellowbox} + x_{65\yellowbox} \le 6v_{5\yellowbox} x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ Column 5, Yellow Patch x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ x_{16\yellowbox} + x_{26\yellowbox} + x_{36\yellowbox} + x_{46\yellowbox} + x_{56\yellowbox} + x_{66\yellowbox} \le 6v_{6\yellowbox} x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ Column 6, Yellow Patch x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ x_{11\tealbox} + x_{21\tealbox} + x_{31\tealbox} + x_{41\tealbox} + x_{51\tealbox} + x_{61\tealbox} \le 6v_{1\tealbox} x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ Column 1, Teal x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ x_{12\tealbox} + x_{22\tealbox} + x_{32\tealbox} + x_{42\tealbox} + x_{52\tealbox} + x_{62\tealbox} \le 6v_{2\tealbox} x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ Column 2, Teal x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ x_{13\tealbox} + x_{23\tealbox} + x_{33\tealbox} + x_{43\tealbox} + x_{53\tealbox} + x_{63\tealbox} \le 6v_{3\tealbox} x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ Column 3, Teal x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ x_{14\tealbox} + x_{24\tealbox} + x_{34\tealbox} + x_{44\tealbox} + x_{54\tealbox} + x_{64\tealbox} \le 6v_{4\tealbox} x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ Column 4, Teal x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ x_{15\tealbox} + x_{25\tealbox} + x_{35\tealbox} + x_{45\tealbox} + x_{55\tealbox} + x_{65\tealbox} \le 6v_{5\tealbox} x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ Column 5, Teal x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ x_{16\tealbox} + x_{26\tealbox} + x_{36\tealbox} + x_{46\tealbox} + x_{56\tealbox} + x_{66\tealbox} \le 6v_{6\tealbox} x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ Column 6, Teal x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ x_{11\purplebox} + x_{21\purplebox} + x_{31\purplebox} + x_{41\purplebox} + x_{51\purplebox} + x_{61\purplebox} \le 6v_{1\purplebox} x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ Column 1, Purple Patch x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ x_{12\purplebox} + x_{22\purplebox} + x_{32\purplebox} + x_{42\purplebox} + x_{52\purplebox} + x_{62\purplebox} \le 6v_{2\purplebox} x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ Column 2, Purple Patch x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ x_{13\purplebox} + x_{23\purplebox} + x_{33\purplebox} + x_{43\purplebox} + x_{53\purplebox} + x_{63\purplebox} \le 6v_{3\purplebox} x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ Column 3, Purple Patch x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ x_{14\purplebox} + x_{24\purplebox} + x_{34\purplebox} + x_{44\purplebox} + x_{54\purplebox} + x_{64\purplebox} \le 6v_{4\purplebox} x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ Column 4, Purple Patch x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ x_{15\purplebox} + x_{25\purplebox} + x_{35\purplebox} + x_{45\purplebox} + x_{55\purplebox} + x_{65\purplebox} \le 6v_{5\purplebox} x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ Column 5, Purple Patch x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ x_{16\purplebox} + x_{26\purplebox} + x_{36\purplebox} + x_{46\purplebox} + x_{56\purplebox} + x_{66\purplebox} \le 6v_{6\purplebox} x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ Column 6, Purple Patch x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ x_{11\greenbox} + x_{21\greenbox} + x_{31\greenbox} + x_{41\greenbox} + x_{51\greenbox} + x_{61\greenbox} \le 6v_{1\greenbox} x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ Column 1, Green Patch x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ x_{12\greenbox} + x_{22\greenbox} + x_{32\greenbox} + x_{42\greenbox} + x_{52\greenbox} + x_{62\greenbox} \le 6v_{2\greenbox} x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ Column 2, Green Patch x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ x_{13\greenbox} + x_{23\greenbox} + x_{33\greenbox} + x_{43\greenbox} + x_{53\greenbox} + x_{63\greenbox} \le 6v_{3\greenbox} x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ Column 3, Green Patch x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ x_{14\greenbox} + x_{24\greenbox} + x_{34\greenbox} + x_{44\greenbox} + x_{54\greenbox} + x_{64\greenbox} \le 6v_{4\greenbox} x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ Column 4, Green Patch x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ x_{15\greenbox} + x_{25\greenbox} + x_{35\greenbox} + x_{45\greenbox} + x_{55\greenbox} + x_{65\greenbox} \le 6v_{5\greenbox} x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ Column 5, Green Patch x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ x_{16\greenbox} + x_{26\greenbox} + x_{36\greenbox} + x_{46\greenbox} + x_{56\greenbox} + x_{66\greenbox} \le 6v_{6\greenbox} x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ Column 6, Green Patch x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ x_{11\orangebox} + x_{21\orangebox} + x_{31\orangebox} + x_{41\orangebox} + x_{51\orangebox} + x_{61\orangebox} \le 6v_{1\orangebox} x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ Column 1, Orange Patch x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ x_{12\orangebox} + x_{22\orangebox} + x_{32\orangebox} + x_{42\orangebox} + x_{52\orangebox} + x_{62\orangebox} \le 6v_{2\orangebox} x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ Column 2, Orange Patch x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ x_{13\orangebox} + x_{23\orangebox} + x_{33\orangebox} + x_{43\orangebox} + x_{53\orangebox} + x_{63\orangebox} \le 6v_{3\orangebox} x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ Column 3, Orange Patch x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ x_{14\orangebox} + x_{24\orangebox} + x_{34\orangebox} + x_{44\orangebox} + x_{54\orangebox} + x_{64\orangebox} \le 6v_{4\orangebox} x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ Column 4, Orange Patch x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ x_{15\orangebox} + x_{25\orangebox} + x_{35\orangebox} + x_{45\orangebox} + x_{55\orangebox} + x_{65\orangebox} \le 6v_{5\orangebox} x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ Column 5, Orange Patch x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ x_{16\orangebox} + x_{26\orangebox} + x_{36\orangebox} + x_{46\orangebox} + x_{56\orangebox} + x_{66\orangebox} \le 6v_{6\orangebox} x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ Column 6, Orange Patch x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ x_{11\redbox} + x_{21\redbox} + x_{31\redbox} + x_{41\redbox} + x_{51\redbox} + x_{61\redbox} \le 6v_{1\redbox} x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ Column 1, Red Patch x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ x_{12\redbox} + x_{22\redbox} + x_{32\redbox} + x_{42\redbox} + x_{52\redbox} + x_{62\redbox} \le 6v_{2\redbox} x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ Column 2, Red Patch x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ x_{13\redbox} + x_{23\redbox} + x_{33\redbox} + x_{43\redbox} + x_{53\redbox} + x_{63\redbox} \le 6v_{3\redbox} x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ Column 3, Red Patch x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ x_{14\redbox} + x_{24\redbox} + x_{34\redbox} + x_{44\redbox} + x_{54\redbox} + x_{64\redbox} \le 6v_{4\redbox} x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ Column 4, Red Patch x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ x_{15\redbox} + x_{25\redbox} + x_{35\redbox} + x_{45\redbox} + x_{55\redbox} + x_{65\redbox} \le 6v_{5\redbox} x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ Column 5, Red Patch x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ x_{16\redbox} + x_{26\redbox} + x_{36\redbox} + x_{46\redbox} + x_{56\redbox} + x_{66\redbox} \le 6v_{6\redbox} x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ Column 6, Red Patch x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ x_{11\bluebox} + x_{21\bluebox} + x_{31\bluebox} + x_{41\bluebox} + x_{51\bluebox} + x_{61\bluebox} \le 6v_{1\bluebox} x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ Column 1, Blue Patch x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ x_{12\bluebox} + x_{22\bluebox} + x_{32\bluebox} + x_{42\bluebox} + x_{52\bluebox} + x_{62\bluebox} \le 6v_{2\bluebox} x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ Column 2, Blue Patch x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ x_{13\bluebox} + x_{23\bluebox} + x_{33\bluebox} + x_{43\bluebox} + x_{53\bluebox} + x_{63\bluebox} \le 6v_{3\bluebox} x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ Column 3, Blue Patch x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ x_{14\bluebox} + x_{24\bluebox} + x_{34\bluebox} + x_{44\bluebox} + x_{54\bluebox} + x_{64\bluebox} \le 6v_{4\bluebox} x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ Column 4, Blue Patch x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ x_{15\bluebox} + x_{25\bluebox} + x_{35\bluebox} + x_{45\bluebox} + x_{55\bluebox} + x_{65\bluebox} \le 6v_{5\bluebox} x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ Column 5, Blue Patch x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ x_{16\bluebox} + x_{26\bluebox} + x_{36\bluebox} + x_{46\bluebox} + x_{56\bluebox} + x_{66\bluebox} \le 6v_{6\bluebox} x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ Column 6, Blue Patch x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ x_{11\magentabox} + x_{21\magentabox} + x_{31\magentabox} + x_{41\magentabox} + x_{51\magentabox} + x_{61\magentabox} \le 6v_{1\magentabox} x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ Column 1, Magenta Patch x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ x_{12\magentabox} + x_{22\magentabox} + x_{32\magentabox} + x_{42\magentabox} + x_{52\magentabox} + x_{62\magentabox} \le 6v_{2\magentabox} x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ Column 2, Magenta Patch x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ x_{13\magentabox} + x_{23\magentabox} + x_{33\magentabox} + x_{43\magentabox} + x_{53\magentabox} + x_{63\magentabox} \le 6v_{3\magentabox} x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ Column 3, Magenta Patch x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ x_{14\magentabox} + x_{24\magentabox} + x_{34\magentabox} + x_{44\magentabox} + x_{54\magentabox} + x_{64\magentabox} \le 6v_{4\magentabox} x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ Column 4, Magenta Patch x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ x_{15\magentabox} + x_{25\magentabox} + x_{35\magentabox} + x_{45\magentabox} + x_{55\magentabox} + x_{65\magentabox} \le 6v_{5\magentabox} x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ Column 5, Magenta Patch x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ x_{16\magentabox} + x_{26\magentabox} + x_{36\magentabox} + x_{46\magentabox} + x_{56\magentabox} + x_{66\magentabox} \le 6v_{6\magentabox} x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ Column 6, Magenta Patch x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ x_{11\brickbox} + x_{21\brickbox} + x_{31\brickbox} + x_{41\brickbox} + x_{51\brickbox} + x_{61\brickbox} \le 6v_{1\brickbox} x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ Column 1, Brick Patch x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ x_{12\brickbox} + x_{22\brickbox} + x_{32\brickbox} + x_{42\brickbox} + x_{52\brickbox} + x_{62\brickbox} \le 6v_{2\brickbox} x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ Column 2, Brick Patch x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ x_{13\brickbox} + x_{23\brickbox} + x_{33\brickbox} + x_{43\brickbox} + x_{53\brickbox} + x_{63\brickbox} \le 6v_{3\brickbox} x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ Column 3, Brick Patch x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ x_{14\brickbox} + x_{24\brickbox} + x_{34\brickbox} + x_{44\brickbox} + x_{54\brickbox} + x_{64\brickbox} \le 6v_{4\brickbox} x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ Column 4, Brick Patch x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ x_{15\brickbox} + x_{25\brickbox} + x_{35\brickbox} + x_{45\brickbox} + x_{55\brickbox} + x_{65\brickbox} \le 6v_{5\brickbox} x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ Column 5, Brick Patch x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ x_{16\brickbox} + x_{26\brickbox} + x_{36\brickbox} + x_{46\brickbox} + x_{56\brickbox} + x_{66\brickbox} \le 6v_{6\brickbox} x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ Column 6, Brick Patch x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ x_{11\brownbox} + x_{21\brownbox} + x_{31\brownbox} + x_{41\brownbox} + x_{51\brownbox} + x_{61\brownbox} \le 6v_{1\brownbox} x 11 ■ + x 21 ■ + x 31 ■ + x 41 ■ + x 51 ■ + x 61 ■ ≤ 6 v 1 ■ Column 1, Brown Patch x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ x_{12\brownbox} + x_{22\brownbox} + x_{32\brownbox} + x_{42\brownbox} + x_{52\brownbox} + x_{62\brownbox} \le 6v_{2\brownbox} x 12 ■ + x 22 ■ + x 32 ■ + x 42 ■ + x 52 ■ + x 62 ■ ≤ 6 v 2 ■ Column 2, Brown Patch x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ x_{13\brownbox} + x_{23\brownbox} + x_{33\brownbox} + x_{43\brownbox} + x_{53\brownbox} + x_{63\brownbox} \le 6v_{3\brownbox} x 13 ■ + x 23 ■ + x 33 ■ + x 43 ■ + x 53 ■ + x 63 ■ ≤ 6 v 3 ■ Column 3, Brown Patch x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ x_{14\brownbox} + x_{24\brownbox} + x_{34\brownbox} + x_{44\brownbox} + x_{54\brownbox} + x_{64\brownbox} \le 6v_{4\brownbox} x 14 ■ + x 24 ■ + x 34 ■ + x 44 ■ + x 54 ■ + x 64 ■ ≤ 6 v 4 ■ Column 4, Brown Patch x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ x_{15\brownbox} + x_{25\brownbox} + x_{35\brownbox} + x_{45\brownbox} + x_{55\brownbox} + x_{65\brownbox} \le 6v_{5\brownbox} x 15 ■ + x 25 ■ + x 35 ■ + x 45 ■ + x 55 ■ + x 65 ■ ≤ 6 v 5 ■ Column 5, Brown Patch x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ x_{16\brownbox} + x_{26\brownbox} + x_{36\brownbox} + x_{46\brownbox} + x_{56\brownbox} + x_{66\brownbox} \le 6v_{6\brownbox} x 16 ■ + x 26 ■ + x 36 ■ + x 46 ■ + x 56 ■ + x 66 ■ ≤ 6 v 6 ■ Column 6, Brown Patch Square Coverage Constraints x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 x_{11\yellowbox} \ge u_{1\yellowbox} + v_{1\yellowbox} - 1 x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 Square (1, 1), Yellow Patch x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 x_{12\yellowbox} \ge u_{1\yellowbox} + v_{2\yellowbox} - 1 x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 Square (1, 2), Yellow Patch x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 x_{13\yellowbox} \ge u_{1\yellowbox} + v_{3\yellowbox} - 1 x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 Square (1, 3), Yellow Patch x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 x_{14\yellowbox} \ge u_{1\yellowbox} + v_{4\yellowbox} - 1 x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 Square (1, 4), Yellow Patch x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 x_{15\yellowbox} \ge u_{1\yellowbox} + v_{5\yellowbox} - 1 x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 Square (1, 5), Yellow Patch x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 x_{16\yellowbox} \ge u_{1\yellowbox} + v_{6\yellowbox} - 1 x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 Square (1, 6), Yellow Patch x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 x_{21\yellowbox} \ge u_{2\yellowbox} + v_{1\yellowbox} - 1 x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 Square (2, 1), Yellow Patch x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 x_{22\yellowbox} \ge u_{2\yellowbox} + v_{2\yellowbox} - 1 x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 Square (2, 2), Yellow Patch x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 x_{23\yellowbox} \ge u_{2\yellowbox} + v_{3\yellowbox} - 1 x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 Square (2, 3), Yellow Patch x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 x_{24\yellowbox} \ge u_{2\yellowbox} + v_{4\yellowbox} - 1 x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 Square (2, 4), Yellow Patch x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 x_{25\yellowbox} \ge u_{2\yellowbox} + v_{5\yellowbox} - 1 x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 Square (2, 5), Yellow Patch x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 x_{26\yellowbox} \ge u_{2\yellowbox} + v_{6\yellowbox} - 1 x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 Square (2, 6), Yellow Patch x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 x_{31\yellowbox} \ge u_{3\yellowbox} + v_{1\yellowbox} - 1 x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 Square (3, 1), Yellow Patch x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 x_{32\yellowbox} \ge u_{3\yellowbox} + v_{2\yellowbox} - 1 x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 Square (3, 2), Yellow Patch x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 x_{33\yellowbox} \ge u_{3\yellowbox} + v_{3\yellowbox} - 1 x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 Square (3, 3), Yellow Patch x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 x_{34\yellowbox} \ge u_{3\yellowbox} + v_{4\yellowbox} - 1 x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 Square (3, 4), Yellow Patch x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 x_{35\yellowbox} \ge u_{3\yellowbox} + v_{5\yellowbox} - 1 x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 Square (3, 5), Yellow Patch x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 x_{36\yellowbox} \ge u_{3\yellowbox} + v_{6\yellowbox} - 1 x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 Square (3, 6), Yellow Patch x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 x_{41\yellowbox} \ge u_{4\yellowbox} + v_{1\yellowbox} - 1 x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 Square (4, 1), Yellow Patch x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 x_{42\yellowbox} \ge u_{4\yellowbox} + v_{2\yellowbox} - 1 x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 Square (4, 2), Yellow Patch x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 x_{43\yellowbox} \ge u_{4\yellowbox} + v_{3\yellowbox} - 1 x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 Square (4, 3), Yellow Patch x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 x_{44\yellowbox} \ge u_{4\yellowbox} + v_{4\yellowbox} - 1 x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 Square (4, 4), Yellow Patch x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 x_{45\yellowbox} \ge u_{4\yellowbox} + v_{5\yellowbox} - 1 x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 Square (4, 5), Yellow Patch x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 x_{46\yellowbox} \ge u_{4\yellowbox} + v_{6\yellowbox} - 1 x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 Square (4, 6), Yellow Patch x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 x_{51\yellowbox} \ge u_{5\yellowbox} + v_{1\yellowbox} - 1 x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 Square (5, 1), Yellow Patch x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 x_{52\yellowbox} \ge u_{5\yellowbox} + v_{2\yellowbox} - 1 x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 Square (5, 2), Yellow Patch x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 x_{53\yellowbox} \ge u_{5\yellowbox} + v_{3\yellowbox} - 1 x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 Square (5, 3), Yellow Patch x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 x_{54\yellowbox} \ge u_{5\yellowbox} + v_{4\yellowbox} - 1 x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 Square (5, 4), Yellow Patch x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 x_{55\yellowbox} \ge u_{5\yellowbox} + v_{5\yellowbox} - 1 x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 Square (5, 5), Yellow Patch x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 x_{56\yellowbox} \ge u_{5\yellowbox} + v_{6\yellowbox} - 1 x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 Square (5, 6), Yellow Patch x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 x_{61\yellowbox} \ge u_{6\yellowbox} + v_{1\yellowbox} - 1 x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 Square (6, 1), Yellow Patch x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 x_{62\yellowbox} \ge u_{6\yellowbox} + v_{2\yellowbox} - 1 x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 Square (6, 2), Yellow Patch x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 x_{63\yellowbox} \ge u_{6\yellowbox} + v_{3\yellowbox} - 1 x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 Square (6, 3), Yellow Patch x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 x_{64\yellowbox} \ge u_{6\yellowbox} + v_{4\yellowbox} - 1 x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 Square (6, 4), Yellow Patch x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 x_{65\yellowbox} \ge u_{6\yellowbox} + v_{5\yellowbox} - 1 x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 Square (6, 5), Yellow Patch x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 x_{66\yellowbox} \ge u_{6\yellowbox} + v_{6\yellowbox} - 1 x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 Square (6, 6), Yellow Patch x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 x_{11\tealbox} \ge u_{1\tealbox} + v_{1\tealbox} - 1 x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 Square (1, 1), Tealbox Patch x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 x_{12\tealbox} \ge u_{1\tealbox} + v_{2\tealbox} - 1 x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 Square (1, 2), Tealbox Patch x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 x_{13\tealbox} \ge u_{1\tealbox} + v_{3\tealbox} - 1 x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 Square (1, 3), Tealbox Patch x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 x_{14\tealbox} \ge u_{1\tealbox} + v_{4\tealbox} - 1 x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 Square (1, 4), Tealbox Patch x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 x_{15\tealbox} \ge u_{1\tealbox} + v_{5\tealbox} - 1 x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 Square (1, 5), Tealbox Patch x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 x_{16\tealbox} \ge u_{1\tealbox} + v_{6\tealbox} - 1 x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 Square (1, 6), Tealbox Patch x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 x_{21\tealbox} \ge u_{2\tealbox} + v_{1\tealbox} - 1 x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 Square (2, 1), Tealbox Patch x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 x_{22\tealbox} \ge u_{2\tealbox} + v_{2\tealbox} - 1 x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 Square (2, 2), Tealbox Patch x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 x_{23\tealbox} \ge u_{2\tealbox} + v_{3\tealbox} - 1 x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 Square (2, 3), Tealbox Patch x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 x_{24\tealbox} \ge u_{2\tealbox} + v_{4\tealbox} - 1 x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 Square (2, 4), Tealbox Patch x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 x_{25\tealbox} \ge u_{2\tealbox} + v_{5\tealbox} - 1 x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 Square (2, 5), Tealbox Patch x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 x_{26\tealbox} \ge u_{2\tealbox} + v_{6\tealbox} - 1 x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 Square (2, 6), Tealbox Patch x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 x_{31\tealbox} \ge u_{3\tealbox} + v_{1\tealbox} - 1 x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 Square (3, 1), Tealbox Patch x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 x_{32\tealbox} \ge u_{3\tealbox} + v_{2\tealbox} - 1 x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 Square (3, 2), Tealbox Patch x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 x_{33\tealbox} \ge u_{3\tealbox} + v_{3\tealbox} - 1 x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 Square (3, 3), Tealbox Patch x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 x_{34\tealbox} \ge u_{3\tealbox} + v_{4\tealbox} - 1 x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 Square (3, 4), Tealbox Patch x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 x_{35\tealbox} \ge u_{3\tealbox} + v_{5\tealbox} - 1 x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 Square (3, 5), Tealbox Patch x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 x_{36\tealbox} \ge u_{3\tealbox} + v_{6\tealbox} - 1 x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 Square (3, 6), Tealbox Patch x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 x_{41\tealbox} \ge u_{4\tealbox} + v_{1\tealbox} - 1 x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 Square (4, 1), Tealbox Patch x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 x_{42\tealbox} \ge u_{4\tealbox} + v_{2\tealbox} - 1 x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 Square (4, 2), Tealbox Patch x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 x_{43\tealbox} \ge u_{4\tealbox} + v_{3\tealbox} - 1 x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 Square (4, 3), Tealbox Patch x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 x_{44\tealbox} \ge u_{4\tealbox} + v_{4\tealbox} - 1 x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 Square (4, 4), Tealbox Patch x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 x_{45\tealbox} \ge u_{4\tealbox} + v_{5\tealbox} - 1 x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 Square (4, 5), Tealbox Patch x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 x_{46\tealbox} \ge u_{4\tealbox} + v_{6\tealbox} - 1 x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 Square (4, 6), Tealbox Patch x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 x_{51\tealbox} \ge u_{5\tealbox} + v_{1\tealbox} - 1 x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 Square (5, 1), Tealbox Patch x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 x_{52\tealbox} \ge u_{5\tealbox} + v_{2\tealbox} - 1 x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 Square (5, 2), Tealbox Patch x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 x_{53\tealbox} \ge u_{5\tealbox} + v_{3\tealbox} - 1 x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 Square (5, 3), Tealbox Patch x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 x_{54\tealbox} \ge u_{5\tealbox} + v_{4\tealbox} - 1 x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 Square (5, 4), Tealbox Patch x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 x_{55\tealbox} \ge u_{5\tealbox} + v_{5\tealbox} - 1 x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 Square (5, 5), Tealbox Patch x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 x_{56\tealbox} \ge u_{5\tealbox} + v_{6\tealbox} - 1 x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 Square (5, 6), Tealbox Patch x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 x_{61\tealbox} \ge u_{6\tealbox} + v_{1\tealbox} - 1 x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 Square (6, 1), Tealbox Patch x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 x_{62\tealbox} \ge u_{6\tealbox} + v_{2\tealbox} - 1 x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 Square (6, 2), Tealbox Patch x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 x_{63\tealbox} \ge u_{6\tealbox} + v_{3\tealbox} - 1 x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 Square (6, 3), Tealbox Patch x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 x_{64\tealbox} \ge u_{6\tealbox} + v_{4\tealbox} - 1 x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 Square (6, 4), Tealbox Patch x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 x_{65\tealbox} \ge u_{6\tealbox} + v_{5\tealbox} - 1 x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 Square (6, 5), Tealbox Patch x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 x_{66\tealbox} \ge u_{6\tealbox} + v_{6\tealbox} - 1 x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 Square (6, 6), Tealbox Patch x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 x_{11\purplebox} \ge u_{1\purplebox} + v_{1\purplebox} - 1 x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 Square (1, 1), Purple Patch x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 x_{12\purplebox} \ge u_{1\purplebox} + v_{2\purplebox} - 1 x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 Square (1, 2), Purple Patch x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 x_{13\purplebox} \ge u_{1\purplebox} + v_{3\purplebox} - 1 x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 Square (1, 3), Purple Patch x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 x_{14\purplebox} \ge u_{1\purplebox} + v_{4\purplebox} - 1 x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 Square (1, 4), Purple Patch x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 x_{15\purplebox} \ge u_{1\purplebox} + v_{5\purplebox} - 1 x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 Square (1, 5), Purple Patch x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 x_{16\purplebox} \ge u_{1\purplebox} + v_{6\purplebox} - 1 x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 Square (1, 6), Purple Patch x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 x_{21\purplebox} \ge u_{2\purplebox} + v_{1\purplebox} - 1 x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 Square (2, 1), Purple Patch x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 x_{22\purplebox} \ge u_{2\purplebox} + v_{2\purplebox} - 1 x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 Square (2, 2), Purple Patch x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 x_{23\purplebox} \ge u_{2\purplebox} + v_{3\purplebox} - 1 x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 Square (2, 3), Purple Patch x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 x_{24\purplebox} \ge u_{2\purplebox} + v_{4\purplebox} - 1 x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 Square (2, 4), Purple Patch x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 x_{25\purplebox} \ge u_{2\purplebox} + v_{5\purplebox} - 1 x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 Square (2, 5), Purple Patch x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 x_{26\purplebox} \ge u_{2\purplebox} + v_{6\purplebox} - 1 x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 Square (2, 6), Purple Patch x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 x_{31\purplebox} \ge u_{3\purplebox} + v_{1\purplebox} - 1 x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 Square (3, 1), Purple Patch x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 x_{32\purplebox} \ge u_{3\purplebox} + v_{2\purplebox} - 1 x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 Square (3, 2), Purple Patch x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 x_{33\purplebox} \ge u_{3\purplebox} + v_{3\purplebox} - 1 x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 Square (3, 3), Purple Patch x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 x_{34\purplebox} \ge u_{3\purplebox} + v_{4\purplebox} - 1 x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 Square (3, 4), Purple Patch x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 x_{35\purplebox} \ge u_{3\purplebox} + v_{5\purplebox} - 1 x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 Square (3, 5), Purple Patch x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 x_{36\purplebox} \ge u_{3\purplebox} + v_{6\purplebox} - 1 x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 Square (3, 6), Purple Patch x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 x_{41\purplebox} \ge u_{4\purplebox} + v_{1\purplebox} - 1 x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 Square (4, 1), Purple Patch x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 x_{42\purplebox} \ge u_{4\purplebox} + v_{2\purplebox} - 1 x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 Square (4, 2), Purple Patch x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 x_{43\purplebox} \ge u_{4\purplebox} + v_{3\purplebox} - 1 x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 Square (4, 3), Purple Patch x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 x_{44\purplebox} \ge u_{4\purplebox} + v_{4\purplebox} - 1 x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 Square (4, 4), Purple Patch x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 x_{45\purplebox} \ge u_{4\purplebox} + v_{5\purplebox} - 1 x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 Square (4, 5), Purple Patch x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 x_{46\purplebox} \ge u_{4\purplebox} + v_{6\purplebox} - 1 x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 Square (4, 6), Purple Patch x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 x_{51\purplebox} \ge u_{5\purplebox} + v_{1\purplebox} - 1 x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 Square (5, 1), Purple Patch x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 x_{52\purplebox} \ge u_{5\purplebox} + v_{2\purplebox} - 1 x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 Square (5, 2), Purple Patch x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 x_{53\purplebox} \ge u_{5\purplebox} + v_{3\purplebox} - 1 x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 Square (5, 3), Purple Patch x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 x_{54\purplebox} \ge u_{5\purplebox} + v_{4\purplebox} - 1 x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 Square (5, 4), Purple Patch x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 x_{55\purplebox} \ge u_{5\purplebox} + v_{5\purplebox} - 1 x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 Square (5, 5), Purple Patch x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 x_{56\purplebox} \ge u_{5\purplebox} + v_{6\purplebox} - 1 x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 Square (5, 6), Purple Patch x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 x_{61\purplebox} \ge u_{6\purplebox} + v_{1\purplebox} - 1 x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 Square (6, 1), Purple Patch x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 x_{62\purplebox} \ge u_{6\purplebox} + v_{2\purplebox} - 1 x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 Square (6, 2), Purple Patch x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 x_{63\purplebox} \ge u_{6\purplebox} + v_{3\purplebox} - 1 x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 Square (6, 3), Purple Patch x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 x_{64\purplebox} \ge u_{6\purplebox} + v_{4\purplebox} - 1 x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 Square (6, 4), Purple Patch x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 x_{65\purplebox} \ge u_{6\purplebox} + v_{5\purplebox} - 1 x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 Square (6, 5), Purple Patch x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 x_{66\purplebox} \ge u_{6\purplebox} + v_{6\purplebox} - 1 x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 Square (6, 6), Purple Patch x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 x_{11\greenbox} \ge u_{1\greenbox} + v_{1\greenbox} - 1 x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 Square (1, 1), Green Patch x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 x_{12\greenbox} \ge u_{1\greenbox} + v_{2\greenbox} - 1 x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 Square (1, 2), Green Patch x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 x_{13\greenbox} \ge u_{1\greenbox} + v_{3\greenbox} - 1 x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 Square (1, 3), Green Patch x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 x_{14\greenbox} \ge u_{1\greenbox} + v_{4\greenbox} - 1 x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 Square (1, 4), Green Patch x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 x_{15\greenbox} \ge u_{1\greenbox} + v_{5\greenbox} - 1 x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 Square (1, 5), Green Patch x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 x_{16\greenbox} \ge u_{1\greenbox} + v_{6\greenbox} - 1 x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 Square (1, 6), Green Patch x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 x_{21\greenbox} \ge u_{2\greenbox} + v_{1\greenbox} - 1 x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 Square (2, 1), Green Patch x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 x_{22\greenbox} \ge u_{2\greenbox} + v_{2\greenbox} - 1 x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 Square (2, 2), Green Patch x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 x_{23\greenbox} \ge u_{2\greenbox} + v_{3\greenbox} - 1 x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 Square (2, 3), Green Patch x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 x_{24\greenbox} \ge u_{2\greenbox} + v_{4\greenbox} - 1 x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 Square (2, 4), Green Patch x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 x_{25\greenbox} \ge u_{2\greenbox} + v_{5\greenbox} - 1 x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 Square (2, 5), Green Patch x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 x_{26\greenbox} \ge u_{2\greenbox} + v_{6\greenbox} - 1 x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 Square (2, 6), Green Patch x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 x_{31\greenbox} \ge u_{3\greenbox} + v_{1\greenbox} - 1 x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 Square (3, 1), Green Patch x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 x_{32\greenbox} \ge u_{3\greenbox} + v_{2\greenbox} - 1 x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 Square (3, 2), Green Patch x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 x_{33\greenbox} \ge u_{3\greenbox} + v_{3\greenbox} - 1 x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 Square (3, 3), Green Patch x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 x_{34\greenbox} \ge u_{3\greenbox} + v_{4\greenbox} - 1 x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 Square (3, 4), Green Patch x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 x_{35\greenbox} \ge u_{3\greenbox} + v_{5\greenbox} - 1 x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 Square (3, 5), Green Patch x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 x_{36\greenbox} \ge u_{3\greenbox} + v_{6\greenbox} - 1 x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 Square (3, 6), Green Patch x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 x_{41\greenbox} \ge u_{4\greenbox} + v_{1\greenbox} - 1 x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 Square (4, 1), Green Patch x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 x_{42\greenbox} \ge u_{4\greenbox} + v_{2\greenbox} - 1 x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 Square (4, 2), Green Patch x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 x_{43\greenbox} \ge u_{4\greenbox} + v_{3\greenbox} - 1 x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 Square (4, 3), Green Patch x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 x_{44\greenbox} \ge u_{4\greenbox} + v_{4\greenbox} - 1 x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 Square (4, 4), Green Patch x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 x_{45\greenbox} \ge u_{4\greenbox} + v_{5\greenbox} - 1 x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 Square (4, 5), Green Patch x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 x_{46\greenbox} \ge u_{4\greenbox} + v_{6\greenbox} - 1 x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 Square (4, 6), Green Patch x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 x_{51\greenbox} \ge u_{5\greenbox} + v_{1\greenbox} - 1 x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 Square (5, 1), Green Patch x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 x_{52\greenbox} \ge u_{5\greenbox} + v_{2\greenbox} - 1 x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 Square (5, 2), Green Patch x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 x_{53\greenbox} \ge u_{5\greenbox} + v_{3\greenbox} - 1 x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 Square (5, 3), Green Patch x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 x_{54\greenbox} \ge u_{5\greenbox} + v_{4\greenbox} - 1 x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 Square (5, 4), Green Patch x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 x_{55\greenbox} \ge u_{5\greenbox} + v_{5\greenbox} - 1 x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 Square (5, 5), Green Patch x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 x_{56\greenbox} \ge u_{5\greenbox} + v_{6\greenbox} - 1 x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 Square (5, 6), Green Patch x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 x_{61\greenbox} \ge u_{6\greenbox} + v_{1\greenbox} - 1 x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 Square (6, 1), Green Patch x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 x_{62\greenbox} \ge u_{6\greenbox} + v_{2\greenbox} - 1 x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 Square (6, 2), Green Patch x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 x_{63\greenbox} \ge u_{6\greenbox} + v_{3\greenbox} - 1 x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 Square (6, 3), Green Patch x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 x_{64\greenbox} \ge u_{6\greenbox} + v_{4\greenbox} - 1 x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 Square (6, 4), Green Patch x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 x_{65\greenbox} \ge u_{6\greenbox} + v_{5\greenbox} - 1 x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 Square (6, 5), Green Patch x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 x_{66\greenbox} \ge u_{6\greenbox} + v_{6\greenbox} - 1 x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 Square (6, 6), Green Patch x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 x_{11\orangebox} \ge u_{1\orangebox} + v_{1\orangebox} - 1 x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 Square (1, 1), Orange Patch x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 x_{12\orangebox} \ge u_{1\orangebox} + v_{2\orangebox} - 1 x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 Square (1, 2), Orange Patch x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 x_{13\orangebox} \ge u_{1\orangebox} + v_{3\orangebox} - 1 x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 Square (1, 3), Orange Patch x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 x_{14\orangebox} \ge u_{1\orangebox} + v_{4\orangebox} - 1 x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 Square (1, 4), Orange Patch x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 x_{15\orangebox} \ge u_{1\orangebox} + v_{5\orangebox} - 1 x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 Square (1, 5), Orange Patch x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 x_{16\orangebox} \ge u_{1\orangebox} + v_{6\orangebox} - 1 x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 Square (1, 6), Orange Patch x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 x_{21\orangebox} \ge u_{2\orangebox} + v_{1\orangebox} - 1 x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 Square (2, 1), Orange Patch x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 x_{22\orangebox} \ge u_{2\orangebox} + v_{2\orangebox} - 1 x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 Square (2, 2), Orange Patch x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 x_{23\orangebox} \ge u_{2\orangebox} + v_{3\orangebox} - 1 x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 Square (2, 3), Orange Patch x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 x_{24\orangebox} \ge u_{2\orangebox} + v_{4\orangebox} - 1 x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 Square (2, 4), Orange Patch x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 x_{25\orangebox} \ge u_{2\orangebox} + v_{5\orangebox} - 1 x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 Square (2, 5), Orange Patch x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 x_{26\orangebox} \ge u_{2\orangebox} + v_{6\orangebox} - 1 x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 Square (2, 6), Orange Patch x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 x_{31\orangebox} \ge u_{3\orangebox} + v_{1\orangebox} - 1 x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 Square (3, 1), Orange Patch x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 x_{32\orangebox} \ge u_{3\orangebox} + v_{2\orangebox} - 1 x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 Square (3, 2), Orange Patch x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 x_{33\orangebox} \ge u_{3\orangebox} + v_{3\orangebox} - 1 x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 Square (3, 3), Orange Patch x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 x_{34\orangebox} \ge u_{3\orangebox} + v_{4\orangebox} - 1 x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 Square (3, 4), Orange Patch x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 x_{35\orangebox} \ge u_{3\orangebox} + v_{5\orangebox} - 1 x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 Square (3, 5), Orange Patch x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 x_{36\orangebox} \ge u_{3\orangebox} + v_{6\orangebox} - 1 x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 Square (3, 6), Orange Patch x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 x_{41\orangebox} \ge u_{4\orangebox} + v_{1\orangebox} - 1 x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 Square (4, 1), Orange Patch x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 x_{42\orangebox} \ge u_{4\orangebox} + v_{2\orangebox} - 1 x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 Square (4, 2), Orange Patch x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 x_{43\orangebox} \ge u_{4\orangebox} + v_{3\orangebox} - 1 x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 Square (4, 3), Orange Patch x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 x_{44\orangebox} \ge u_{4\orangebox} + v_{4\orangebox} - 1 x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 Square (4, 4), Orange Patch x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 x_{45\orangebox} \ge u_{4\orangebox} + v_{5\orangebox} - 1 x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 Square (4, 5), Orange Patch x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 x_{46\orangebox} \ge u_{4\orangebox} + v_{6\orangebox} - 1 x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 Square (4, 6), Orange Patch x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 x_{51\orangebox} \ge u_{5\orangebox} + v_{1\orangebox} - 1 x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 Square (5, 1), Orange Patch x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 x_{52\orangebox} \ge u_{5\orangebox} + v_{2\orangebox} - 1 x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 Square (5, 2), Orange Patch x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 x_{53\orangebox} \ge u_{5\orangebox} + v_{3\orangebox} - 1 x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 Square (5, 3), Orange Patch x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 x_{54\orangebox} \ge u_{5\orangebox} + v_{4\orangebox} - 1 x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 Square (5, 4), Orange Patch x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 x_{55\orangebox} \ge u_{5\orangebox} + v_{5\orangebox} - 1 x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 Square (5, 5), Orange Patch x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 x_{56\orangebox} \ge u_{5\orangebox} + v_{6\orangebox} - 1 x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 Square (5, 6), Orange Patch x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 x_{61\orangebox} \ge u_{6\orangebox} + v_{1\orangebox} - 1 x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 Square (6, 1), Orange Patch x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 x_{62\orangebox} \ge u_{6\orangebox} + v_{2\orangebox} - 1 x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 Square (6, 2), Orange Patch x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 x_{63\orangebox} \ge u_{6\orangebox} + v_{3\orangebox} - 1 x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 Square (6, 3), Orange Patch x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 x_{64\orangebox} \ge u_{6\orangebox} + v_{4\orangebox} - 1 x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 Square (6, 4), Orange Patch x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 x_{65\orangebox} \ge u_{6\orangebox} + v_{5\orangebox} - 1 x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 Square (6, 5), Orange Patch x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 x_{66\orangebox} \ge u_{6\orangebox} + v_{6\orangebox} - 1 x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 Square (6, 6), Orange Patch x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 x_{11\redbox} \ge u_{1\redbox} + v_{1\redbox} - 1 x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 Square (1, 1), Red Patch x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 x_{12\redbox} \ge u_{1\redbox} + v_{2\redbox} - 1 x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 Square (1, 2), Red Patch x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 x_{13\redbox} \ge u_{1\redbox} + v_{3\redbox} - 1 x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 Square (1, 3), Red Patch x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 x_{14\redbox} \ge u_{1\redbox} + v_{4\redbox} - 1 x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 Square (1, 4), Red Patch x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 x_{15\redbox} \ge u_{1\redbox} + v_{5\redbox} - 1 x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 Square (1, 5), Red Patch x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 x_{16\redbox} \ge u_{1\redbox} + v_{6\redbox} - 1 x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 Square (1, 6), Red Patch x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 x_{21\redbox} \ge u_{2\redbox} + v_{1\redbox} - 1 x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 Square (2, 1), Red Patch x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 x_{22\redbox} \ge u_{2\redbox} + v_{2\redbox} - 1 x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 Square (2, 2), Red Patch x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 x_{23\redbox} \ge u_{2\redbox} + v_{3\redbox} - 1 x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 Square (2, 3), Red Patch x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 x_{24\redbox} \ge u_{2\redbox} + v_{4\redbox} - 1 x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 Square (2, 4), Red Patch x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 x_{25\redbox} \ge u_{2\redbox} + v_{5\redbox} - 1 x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 Square (2, 5), Red Patch x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 x_{26\redbox} \ge u_{2\redbox} + v_{6\redbox} - 1 x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 Square (2, 6), Red Patch x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 x_{31\redbox} \ge u_{3\redbox} + v_{1\redbox} - 1 x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 Square (3, 1), Red Patch x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 x_{32\redbox} \ge u_{3\redbox} + v_{2\redbox} - 1 x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 Square (3, 2), Red Patch x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 x_{33\redbox} \ge u_{3\redbox} + v_{3\redbox} - 1 x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 Square (3, 3), Red Patch x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 x_{34\redbox} \ge u_{3\redbox} + v_{4\redbox} - 1 x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 Square (3, 4), Red Patch x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 x_{35\redbox} \ge u_{3\redbox} + v_{5\redbox} - 1 x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 Square (3, 5), Red Patch x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 x_{36\redbox} \ge u_{3\redbox} + v_{6\redbox} - 1 x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 Square (3, 6), Red Patch x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 x_{41\redbox} \ge u_{4\redbox} + v_{1\redbox} - 1 x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 Square (4, 1), Red Patch x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 x_{42\redbox} \ge u_{4\redbox} + v_{2\redbox} - 1 x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 Square (4, 2), Red Patch x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 x_{43\redbox} \ge u_{4\redbox} + v_{3\redbox} - 1 x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 Square (4, 3), Red Patch x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 x_{44\redbox} \ge u_{4\redbox} + v_{4\redbox} - 1 x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 Square (4, 4), Red Patch x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 x_{45\redbox} \ge u_{4\redbox} + v_{5\redbox} - 1 x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 Square (4, 5), Red Patch x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 x_{46\redbox} \ge u_{4\redbox} + v_{6\redbox} - 1 x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 Square (4, 6), Red Patch x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 x_{51\redbox} \ge u_{5\redbox} + v_{1\redbox} - 1 x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 Square (5, 1), Red Patch x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 x_{52\redbox} \ge u_{5\redbox} + v_{2\redbox} - 1 x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 Square (5, 2), Red Patch x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 x_{53\redbox} \ge u_{5\redbox} + v_{3\redbox} - 1 x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 Square (5, 3), Red Patch x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 x_{54\redbox} \ge u_{5\redbox} + v_{4\redbox} - 1 x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 Square (5, 4), Red Patch x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 x_{55\redbox} \ge u_{5\redbox} + v_{5\redbox} - 1 x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 Square (5, 5), Red Patch x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 x_{56\redbox} \ge u_{5\redbox} + v_{6\redbox} - 1 x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 Square (5, 6), Red Patch x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 x_{61\redbox} \ge u_{6\redbox} + v_{1\redbox} - 1 x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 Square (6, 1), Red Patch x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 x_{62\redbox} \ge u_{6\redbox} + v_{2\redbox} - 1 x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 Square (6, 2), Red Patch x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 x_{63\redbox} \ge u_{6\redbox} + v_{3\redbox} - 1 x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 Square (6, 3), Red Patch x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 x_{64\redbox} \ge u_{6\redbox} + v_{4\redbox} - 1 x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 Square (6, 4), Red Patch x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 x_{65\redbox} \ge u_{6\redbox} + v_{5\redbox} - 1 x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 Square (6, 5), Red Patch x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 x_{66\redbox} \ge u_{6\redbox} + v_{6\redbox} - 1 x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 Square (6, 6), Red Patch x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 x_{11\bluebox} \ge u_{1\bluebox} + v_{1\bluebox} - 1 x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 Square (1, 1), Blue Patch x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 x_{12\bluebox} \ge u_{1\bluebox} + v_{2\bluebox} - 1 x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 Square (1, 2), Blue Patch x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 x_{13\bluebox} \ge u_{1\bluebox} + v_{3\bluebox} - 1 x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 Square (1, 3), Blue Patch x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 x_{14\bluebox} \ge u_{1\bluebox} + v_{4\bluebox} - 1 x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 Square (1, 4), Blue Patch x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 x_{15\bluebox} \ge u_{1\bluebox} + v_{5\bluebox} - 1 x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 Square (1, 5), Blue Patch x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 x_{16\bluebox} \ge u_{1\bluebox} + v_{6\bluebox} - 1 x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 Square (1, 6), Blue Patch x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 x_{21\bluebox} \ge u_{2\bluebox} + v_{1\bluebox} - 1 x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 Square (2, 1), Blue Patch x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 x_{22\bluebox} \ge u_{2\bluebox} + v_{2\bluebox} - 1 x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 Square (2, 2), Blue Patch x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 x_{23\bluebox} \ge u_{2\bluebox} + v_{3\bluebox} - 1 x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 Square (2, 3), Blue Patch x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 x_{24\bluebox} \ge u_{2\bluebox} + v_{4\bluebox} - 1 x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 Square (2, 4), Blue Patch x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 x_{25\bluebox} \ge u_{2\bluebox} + v_{5\bluebox} - 1 x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 Square (2, 5), Blue Patch x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 x_{26\bluebox} \ge u_{2\bluebox} + v_{6\bluebox} - 1 x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 Square (2, 6), Blue Patch x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 x_{31\bluebox} \ge u_{3\bluebox} + v_{1\bluebox} - 1 x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 Square (3, 1), Blue Patch x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 x_{32\bluebox} \ge u_{3\bluebox} + v_{2\bluebox} - 1 x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 Square (3, 2), Blue Patch x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 x_{33\bluebox} \ge u_{3\bluebox} + v_{3\bluebox} - 1 x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 Square (3, 3), Blue Patch x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 x_{34\bluebox} \ge u_{3\bluebox} + v_{4\bluebox} - 1 x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 Square (3, 4), Blue Patch x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 x_{35\bluebox} \ge u_{3\bluebox} + v_{5\bluebox} - 1 x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 Square (3, 5), Blue Patch x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 x_{36\bluebox} \ge u_{3\bluebox} + v_{6\bluebox} - 1 x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 Square (3, 6), Blue Patch x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 x_{41\bluebox} \ge u_{4\bluebox} + v_{1\bluebox} - 1 x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 Square (4, 1), Blue Patch x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 x_{42\bluebox} \ge u_{4\bluebox} + v_{2\bluebox} - 1 x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 Square (4, 2), Blue Patch x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 x_{43\bluebox} \ge u_{4\bluebox} + v_{3\bluebox} - 1 x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 Square (4, 3), Blue Patch x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 x_{44\bluebox} \ge u_{4\bluebox} + v_{4\bluebox} - 1 x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 Square (4, 4), Blue Patch x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 x_{45\bluebox} \ge u_{4\bluebox} + v_{5\bluebox} - 1 x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 Square (4, 5), Blue Patch x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 x_{46\bluebox} \ge u_{4\bluebox} + v_{6\bluebox} - 1 x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 Square (4, 6), Blue Patch x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 x_{51\bluebox} \ge u_{5\bluebox} + v_{1\bluebox} - 1 x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 Square (5, 1), Blue Patch x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 x_{52\bluebox} \ge u_{5\bluebox} + v_{2\bluebox} - 1 x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 Square (5, 2), Blue Patch x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 x_{53\bluebox} \ge u_{5\bluebox} + v_{3\bluebox} - 1 x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 Square (5, 3), Blue Patch x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 x_{54\bluebox} \ge u_{5\bluebox} + v_{4\bluebox} - 1 x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 Square (5, 4), Blue Patch x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 x_{55\bluebox} \ge u_{5\bluebox} + v_{5\bluebox} - 1 x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 Square (5, 5), Blue Patch x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 x_{56\bluebox} \ge u_{5\bluebox} + v_{6\bluebox} - 1 x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 Square (5, 6), Blue Patch x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 x_{61\bluebox} \ge u_{6\bluebox} + v_{1\bluebox} - 1 x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 Square (6, 1), Blue Patch x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 x_{62\bluebox} \ge u_{6\bluebox} + v_{2\bluebox} - 1 x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 Square (6, 2), Blue Patch x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 x_{63\bluebox} \ge u_{6\bluebox} + v_{3\bluebox} - 1 x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 Square (6, 3), Blue Patch x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 x_{64\bluebox} \ge u_{6\bluebox} + v_{4\bluebox} - 1 x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 Square (6, 4), Blue Patch x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 x_{65\bluebox} \ge u_{6\bluebox} + v_{5\bluebox} - 1 x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 Square (6, 5), Blue Patch x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 x_{66\bluebox} \ge u_{6\bluebox} + v_{6\bluebox} - 1 x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 Square (6, 6), Blue Patch x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 x_{11\magentabox} \ge u_{1\magentabox} + v_{1\magentabox} - 1 x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 Square (1, 1), Magenta Patch x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 x_{12\magentabox} \ge u_{1\magentabox} + v_{2\magentabox} - 1 x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 Square (1, 2), Magenta Patch x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 x_{13\magentabox} \ge u_{1\magentabox} + v_{3\magentabox} - 1 x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 Square (1, 3), Magenta Patch x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 x_{14\magentabox} \ge u_{1\magentabox} + v_{4\magentabox} - 1 x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 Square (1, 4), Magenta Patch x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 x_{15\magentabox} \ge u_{1\magentabox} + v_{5\magentabox} - 1 x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 Square (1, 5), Magenta Patch x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 x_{16\magentabox} \ge u_{1\magentabox} + v_{6\magentabox} - 1 x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 Square (1, 6), Magenta Patch x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 x_{21\magentabox} \ge u_{2\magentabox} + v_{1\magentabox} - 1 x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 Square (2, 1), Magenta Patch x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 x_{22\magentabox} \ge u_{2\magentabox} + v_{2\magentabox} - 1 x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 Square (2, 2), Magenta Patch x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 x_{23\magentabox} \ge u_{2\magentabox} + v_{3\magentabox} - 1 x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 Square (2, 3), Magenta Patch x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 x_{24\magentabox} \ge u_{2\magentabox} + v_{4\magentabox} - 1 x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 Square (2, 4), Magenta Patch x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 x_{25\magentabox} \ge u_{2\magentabox} + v_{5\magentabox} - 1 x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 Square (2, 5), Magenta Patch x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 x_{26\magentabox} \ge u_{2\magentabox} + v_{6\magentabox} - 1 x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 Square (2, 6), Magenta Patch x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 x_{31\magentabox} \ge u_{3\magentabox} + v_{1\magentabox} - 1 x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 Square (3, 1), Magenta Patch x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 x_{32\magentabox} \ge u_{3\magentabox} + v_{2\magentabox} - 1 x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 Square (3, 2), Magenta Patch x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 x_{33\magentabox} \ge u_{3\magentabox} + v_{3\magentabox} - 1 x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 Square (3, 3), Magenta Patch x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 x_{34\magentabox} \ge u_{3\magentabox} + v_{4\magentabox} - 1 x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 Square (3, 4), Magenta Patch x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 x_{35\magentabox} \ge u_{3\magentabox} + v_{5\magentabox} - 1 x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 Square (3, 5), Magenta Patch x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 x_{36\magentabox} \ge u_{3\magentabox} + v_{6\magentabox} - 1 x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 Square (3, 6), Magenta Patch x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 x_{41\magentabox} \ge u_{4\magentabox} + v_{1\magentabox} - 1 x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 Square (4, 1), Magenta Patch x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 x_{42\magentabox} \ge u_{4\magentabox} + v_{2\magentabox} - 1 x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 Square (4, 2), Magenta Patch x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 x_{43\magentabox} \ge u_{4\magentabox} + v_{3\magentabox} - 1 x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 Square (4, 3), Magenta Patch x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 x_{44\magentabox} \ge u_{4\magentabox} + v_{4\magentabox} - 1 x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 Square (4, 4), Magenta Patch x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 x_{45\magentabox} \ge u_{4\magentabox} + v_{5\magentabox} - 1 x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 Square (4, 5), Magenta Patch x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 x_{46\magentabox} \ge u_{4\magentabox} + v_{6\magentabox} - 1 x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 Square (4, 6), Magenta Patch x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 x_{51\magentabox} \ge u_{5\magentabox} + v_{1\magentabox} - 1 x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 Square (5, 1), Magenta Patch x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 x_{52\magentabox} \ge u_{5\magentabox} + v_{2\magentabox} - 1 x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 Square (5, 2), Magenta Patch x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 x_{53\magentabox} \ge u_{5\magentabox} + v_{3\magentabox} - 1 x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 Square (5, 3), Magenta Patch x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 x_{54\magentabox} \ge u_{5\magentabox} + v_{4\magentabox} - 1 x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 Square (5, 4), Magenta Patch x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 x_{55\magentabox} \ge u_{5\magentabox} + v_{5\magentabox} - 1 x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 Square (5, 5), Magenta Patch x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 x_{56\magentabox} \ge u_{5\magentabox} + v_{6\magentabox} - 1 x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 Square (5, 6), Magenta Patch x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 x_{61\magentabox} \ge u_{6\magentabox} + v_{1\magentabox} - 1 x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 Square (6, 1), Magenta Patch x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 x_{62\magentabox} \ge u_{6\magentabox} + v_{2\magentabox} - 1 x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 Square (6, 2), Magenta Patch x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 x_{63\magentabox} \ge u_{6\magentabox} + v_{3\magentabox} - 1 x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 Square (6, 3), Magenta Patch x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 x_{64\magentabox} \ge u_{6\magentabox} + v_{4\magentabox} - 1 x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 Square (6, 4), Magenta Patch x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 x_{65\magentabox} \ge u_{6\magentabox} + v_{5\magentabox} - 1 x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 Square (6, 5), Magenta Patch x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 x_{66\magentabox} \ge u_{6\magentabox} + v_{6\magentabox} - 1 x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 Square (6, 6), Magenta Patch x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 x_{11\brickbox} \ge u_{1\brickbox} + v_{1\brickbox} - 1 x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 Square (1, 1), Brick Patch x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 x_{12\brickbox} \ge u_{1\brickbox} + v_{2\brickbox} - 1 x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 Square (1, 2), Brick Patch x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 x_{13\brickbox} \ge u_{1\brickbox} + v_{3\brickbox} - 1 x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 Square (1, 3), Brick Patch x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 x_{14\brickbox} \ge u_{1\brickbox} + v_{4\brickbox} - 1 x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 Square (1, 4), Brick Patch x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 x_{15\brickbox} \ge u_{1\brickbox} + v_{5\brickbox} - 1 x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 Square (1, 5), Brick Patch x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 x_{16\brickbox} \ge u_{1\brickbox} + v_{6\brickbox} - 1 x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 Square (1, 6), Brick Patch x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 x_{21\brickbox} \ge u_{2\brickbox} + v_{1\brickbox} - 1 x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 Square (2, 1), Brick Patch x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 x_{22\brickbox} \ge u_{2\brickbox} + v_{2\brickbox} - 1 x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 Square (2, 2), Brick Patch x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 x_{23\brickbox} \ge u_{2\brickbox} + v_{3\brickbox} - 1 x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 Square (2, 3), Brick Patch x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 x_{24\brickbox} \ge u_{2\brickbox} + v_{4\brickbox} - 1 x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 Square (2, 4), Brick Patch x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 x_{25\brickbox} \ge u_{2\brickbox} + v_{5\brickbox} - 1 x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 Square (2, 5), Brick Patch x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 x_{26\brickbox} \ge u_{2\brickbox} + v_{6\brickbox} - 1 x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 Square (2, 6), Brick Patch x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 x_{31\brickbox} \ge u_{3\brickbox} + v_{1\brickbox} - 1 x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 Square (3, 1), Brick Patch x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 x_{32\brickbox} \ge u_{3\brickbox} + v_{2\brickbox} - 1 x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 Square (3, 2), Brick Patch x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 x_{33\brickbox} \ge u_{3\brickbox} + v_{3\brickbox} - 1 x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 Square (3, 3), Brick Patch x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 x_{34\brickbox} \ge u_{3\brickbox} + v_{4\brickbox} - 1 x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 Square (3, 4), Brick Patch x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 x_{35\brickbox} \ge u_{3\brickbox} + v_{5\brickbox} - 1 x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 Square (3, 5), Brick Patch x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 x_{36\brickbox} \ge u_{3\brickbox} + v_{6\brickbox} - 1 x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 Square (3, 6), Brick Patch x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 x_{41\brickbox} \ge u_{4\brickbox} + v_{1\brickbox} - 1 x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 Square (4, 1), Brick Patch x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 x_{42\brickbox} \ge u_{4\brickbox} + v_{2\brickbox} - 1 x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 Square (4, 2), Brick Patch x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 x_{43\brickbox} \ge u_{4\brickbox} + v_{3\brickbox} - 1 x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 Square (4, 3), Brick Patch x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 x_{44\brickbox} \ge u_{4\brickbox} + v_{4\brickbox} - 1 x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 Square (4, 4), Brick Patch x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 x_{45\brickbox} \ge u_{4\brickbox} + v_{5\brickbox} - 1 x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 Square (4, 5), Brick Patch x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 x_{46\brickbox} \ge u_{4\brickbox} + v_{6\brickbox} - 1 x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 Square (4, 6), Brick Patch x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 x_{51\brickbox} \ge u_{5\brickbox} + v_{1\brickbox} - 1 x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 Square (5, 1), Brick Patch x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 x_{52\brickbox} \ge u_{5\brickbox} + v_{2\brickbox} - 1 x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 Square (5, 2), Brick Patch x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 x_{53\brickbox} \ge u_{5\brickbox} + v_{3\brickbox} - 1 x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 Square (5, 3), Brick Patch x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 x_{54\brickbox} \ge u_{5\brickbox} + v_{4\brickbox} - 1 x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 Square (5, 4), Brick Patch x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 x_{55\brickbox} \ge u_{5\brickbox} + v_{5\brickbox} - 1 x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 Square (5, 5), Brick Patch x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 x_{56\brickbox} \ge u_{5\brickbox} + v_{6\brickbox} - 1 x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 Square (5, 6), Brick Patch x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 x_{61\brickbox} \ge u_{6\brickbox} + v_{1\brickbox} - 1 x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 Square (6, 1), Brick Patch x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 x_{62\brickbox} \ge u_{6\brickbox} + v_{2\brickbox} - 1 x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 Square (6, 2), Brick Patch x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 x_{63\brickbox} \ge u_{6\brickbox} + v_{3\brickbox} - 1 x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 Square (6, 3), Brick Patch x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 x_{64\brickbox} \ge u_{6\brickbox} + v_{4\brickbox} - 1 x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 Square (6, 4), Brick Patch x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 x_{65\brickbox} \ge u_{6\brickbox} + v_{5\brickbox} - 1 x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 Square (6, 5), Brick Patch x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 x_{66\brickbox} \ge u_{6\brickbox} + v_{6\brickbox} - 1 x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 Square (6, 6), Brick Patch x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 x_{11\brownbox} \ge u_{1\brownbox} + v_{1\brownbox} - 1 x 11 ■ ≥ u 1 ■ + v 1 ■ − 1 Square (1, 1), Brown Patch x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 x_{12\brownbox} \ge u_{1\brownbox} + v_{2\brownbox} - 1 x 12 ■ ≥ u 1 ■ + v 2 ■ − 1 Square (1, 2), Brown Patch x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 x_{13\brownbox} \ge u_{1\brownbox} + v_{3\brownbox} - 1 x 13 ■ ≥ u 1 ■ + v 3 ■ − 1 Square (1, 3), Brown Patch x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 x_{14\brownbox} \ge u_{1\brownbox} + v_{4\brownbox} - 1 x 14 ■ ≥ u 1 ■ + v 4 ■ − 1 Square (1, 4), Brown Patch x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 x_{15\brownbox} \ge u_{1\brownbox} + v_{5\brownbox} - 1 x 15 ■ ≥ u 1 ■ + v 5 ■ − 1 Square (1, 5), Brown Patch x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 x_{16\brownbox} \ge u_{1\brownbox} + v_{6\brownbox} - 1 x 16 ■ ≥ u 1 ■ + v 6 ■ − 1 Square (1, 6), Brown Patch x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 x_{21\brownbox} \ge u_{2\brownbox} + v_{1\brownbox} - 1 x 21 ■ ≥ u 2 ■ + v 1 ■ − 1 Square (2, 1), Brown Patch x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 x_{22\brownbox} \ge u_{2\brownbox} + v_{2\brownbox} - 1 x 22 ■ ≥ u 2 ■ + v 2 ■ − 1 Square (2, 2), Brown Patch x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 x_{23\brownbox} \ge u_{2\brownbox} + v_{3\brownbox} - 1 x 23 ■ ≥ u 2 ■ + v 3 ■ − 1 Square (2, 3), Brown Patch x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 x_{24\brownbox} \ge u_{2\brownbox} + v_{4\brownbox} - 1 x 24 ■ ≥ u 2 ■ + v 4 ■ − 1 Square (2, 4), Brown Patch x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 x_{25\brownbox} \ge u_{2\brownbox} + v_{5\brownbox} - 1 x 25 ■ ≥ u 2 ■ + v 5 ■ − 1 Square (2, 5), Brown Patch x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 x_{26\brownbox} \ge u_{2\brownbox} + v_{6\brownbox} - 1 x 26 ■ ≥ u 2 ■ + v 6 ■ − 1 Square (2, 6), Brown Patch x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 x_{31\brownbox} \ge u_{3\brownbox} + v_{1\brownbox} - 1 x 31 ■ ≥ u 3 ■ + v 1 ■ − 1 Square (3, 1), Brown Patch x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 x_{32\brownbox} \ge u_{3\brownbox} + v_{2\brownbox} - 1 x 32 ■ ≥ u 3 ■ + v 2 ■ − 1 Square (3, 2), Brown Patch x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 x_{33\brownbox} \ge u_{3\brownbox} + v_{3\brownbox} - 1 x 33 ■ ≥ u 3 ■ + v 3 ■ − 1 Square (3, 3), Brown Patch x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 x_{34\brownbox} \ge u_{3\brownbox} + v_{4\brownbox} - 1 x 34 ■ ≥ u 3 ■ + v 4 ■ − 1 Square (3, 4), Brown Patch x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 x_{35\brownbox} \ge u_{3\brownbox} + v_{5\brownbox} - 1 x 35 ■ ≥ u 3 ■ + v 5 ■ − 1 Square (3, 5), Brown Patch x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 x_{36\brownbox} \ge u_{3\brownbox} + v_{6\brownbox} - 1 x 36 ■ ≥ u 3 ■ + v 6 ■ − 1 Square (3, 6), Brown Patch x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 x_{41\brownbox} \ge u_{4\brownbox} + v_{1\brownbox} - 1 x 41 ■ ≥ u 4 ■ + v 1 ■ − 1 Square (4, 1), Brown Patch x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 x_{42\brownbox} \ge u_{4\brownbox} + v_{2\brownbox} - 1 x 42 ■ ≥ u 4 ■ + v 2 ■ − 1 Square (4, 2), Brown Patch x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 x_{43\brownbox} \ge u_{4\brownbox} + v_{3\brownbox} - 1 x 43 ■ ≥ u 4 ■ + v 3 ■ − 1 Square (4, 3), Brown Patch x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 x_{44\brownbox} \ge u_{4\brownbox} + v_{4\brownbox} - 1 x 44 ■ ≥ u 4 ■ + v 4 ■ − 1 Square (4, 4), Brown Patch x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 x_{45\brownbox} \ge u_{4\brownbox} + v_{5\brownbox} - 1 x 45 ■ ≥ u 4 ■ + v 5 ■ − 1 Square (4, 5), Brown Patch x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 x_{46\brownbox} \ge u_{4\brownbox} + v_{6\brownbox} - 1 x 46 ■ ≥ u 4 ■ + v 6 ■ − 1 Square (4, 6), Brown Patch x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 x_{51\brownbox} \ge u_{5\brownbox} + v_{1\brownbox} - 1 x 51 ■ ≥ u 5 ■ + v 1 ■ − 1 Square (5, 1), Brown Patch x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 x_{52\brownbox} \ge u_{5\brownbox} + v_{2\brownbox} - 1 x 52 ■ ≥ u 5 ■ + v 2 ■ − 1 Square (5, 2), Brown Patch x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 x_{53\brownbox} \ge u_{5\brownbox} + v_{3\brownbox} - 1 x 53 ■ ≥ u 5 ■ + v 3 ■ − 1 Square (5, 3), Brown Patch x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 x_{54\brownbox} \ge u_{5\brownbox} + v_{4\brownbox} - 1 x 54 ■ ≥ u 5 ■ + v 4 ■ − 1 Square (5, 4), Brown Patch x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 x_{55\brownbox} \ge u_{5\brownbox} + v_{5\brownbox} - 1 x 55 ■ ≥ u 5 ■ + v 5 ■ − 1 Square (5, 5), Brown Patch x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 x_{56\brownbox} \ge u_{5\brownbox} + v_{6\brownbox} - 1 x 56 ■ ≥ u 5 ■ + v 6 ■ − 1 Square (5, 6), Brown Patch x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 x_{61\brownbox} \ge u_{6\brownbox} + v_{1\brownbox} - 1 x 61 ■ ≥ u 6 ■ + v 1 ■ − 1 Square (6, 1), Brown Patch x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 x_{62\brownbox} \ge u_{6\brownbox} + v_{2\brownbox} - 1 x 62 ■ ≥ u 6 ■ + v 2 ■ − 1 Square (6, 2), Brown Patch x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 x_{63\brownbox} \ge u_{6\brownbox} + v_{3\brownbox} - 1 x 63 ■ ≥ u 6 ■ + v 3 ■ − 1 Square (6, 3), Brown Patch x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 x_{64\brownbox} \ge u_{6\brownbox} + v_{4\brownbox} - 1 x 64 ■ ≥ u 6 ■ + v 4 ■ − 1 Square (6, 4), Brown Patch x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 x_{65\brownbox} \ge u_{6\brownbox} + v_{5\brownbox} - 1 x 65 ■ ≥ u 6 ■ + v 5 ■ − 1 Square (6, 5), Brown Patch x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 x_{66\brownbox} \ge u_{6\brownbox} + v_{6\brownbox} - 1 x 66 ■ ≥ u 6 ■ + v 6 ■ − 1 Square (6, 6), Brown Patch Seed Square Coverage Constraints x 12 ■ = 1 x_{12\yellowbox} = 1 x 12 ■ = 1 Yellow Square x 14 ■ = 1 x_{14\tealbox} = 1 x 14 ■ = 1 Teal Square x 26 ■ = 1 x_{26\purplebox} = 1 x 26 ■ = 1 Purple Square x 31 ■ = 1 x_{31\tealbox} = 1 x 31 ■ = 1 Green Square x 33 ■ = 1 x_{33\orangebox} = 1 x 33 ■ = 1 Orange Square x 44 ■ = 1 x_{44\redbox} = 1 x 44 ■ = 1 Red Square x 46 ■ = 1 x_{46\bluebox} = 1 x 46 ■ = 1 Blue Square x 51 ■ = 1 x_{51\magentabox} = 1 x 51 ■ = 1 Magenta Square x 63 ■ = 1 x_{63\brickbox} = 1 x 63 ■ = 1 Brick Square x 65 ■ = 1 x_{65\brownbox} = 1 x 65 ■ = 1 Brown Square Area Constraints x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 2 x_{11\yellowbox} + x_{12\yellowbox} + x_{13\yellowbox} + x_{14\yellowbox} + x_{15\yellowbox} + x_{16\yellowbox} + x_{21\yellowbox} + x_{22\yellowbox} + x_{23\yellowbox} + x_{24\yellowbox} + x_{25\yellowbox} + x_{26\yellowbox} + x_{31\yellowbox} + x_{32\yellowbox} + x_{33\yellowbox} + x_{34\yellowbox} + x_{35\yellowbox} + x_{36\yellowbox} + x_{41\yellowbox} + x_{42\yellowbox} + x_{43\yellowbox} + x_{44\yellowbox} + x_{45\yellowbox} + x_{46\yellowbox} + x_{51\yellowbox} + x_{52\yellowbox} + x_{53\yellowbox} + x_{54\yellowbox} + x_{55\yellowbox} + x_{56\yellowbox} + x_{61\yellowbox} + x_{62\yellowbox} + x_{63\yellowbox} + x_{64\yellowbox} + x_{65\yellowbox} + x_{66\yellowbox} = 2 x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 2 Yellow Patch x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 6 x_{11\tealbox} + x_{12\tealbox} + x_{13\tealbox} + x_{14\tealbox} + x_{15\tealbox} + x_{16\tealbox} + x_{21\tealbox} + x_{22\tealbox} + x_{23\tealbox} + x_{24\tealbox} + x_{25\tealbox}+ x_{26\tealbox} + x_{31\tealbox} + x_{32\tealbox} + x_{33\tealbox} + x_{34\tealbox} + x_{35\tealbox} + x_{36\tealbox} + x_{41\tealbox} + x_{42\tealbox} + x_{43\tealbox} + x_{44\tealbox} +x_{45\tealbox} + x_{46\tealbox} + x_{51\tealbox} + x_{52\tealbox} + x_{53\tealbox} + x_{54\tealbox} + x_{55\tealbox} + x_{56\tealbox} + x_{61\tealbox} + x_{62\tealbox} + x_{63\tealbox} + x_{64\tealbox} + x_{65\tealbox} + x_{66\tealbox} = 6 x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 6 Teal Patch x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 2 x_{11\purplebox} + x_{12\purplebox} + x_{13\purplebox} + x_{14\purplebox} + x_{15\purplebox} + x_{16\purplebox} + x_{21\purplebox} + x_{22\purplebox} + x_{23\purplebox} + x_{24\purplebox} + x_{25\purplebox} + x_{26\purplebox} + x_{31\purplebox} + x_{32\purplebox} + x_{33\purplebox} + x_{34\purplebox} + x_{35\purplebox} + x_{36\purplebox} + x_{41\purplebox} + x_{42\purplebox} + x_{43\purplebox} + x_{44\purplebox} + x_{45\purplebox} + x_{46\purplebox} + x_{51\purplebox} + x_{52\purplebox} + x_{53\purplebox} + x_{54\purplebox} + x_{55\purplebox} + x_{56\purplebox} + x_{61\purplebox} + x_{62\purplebox} + x_{63\purplebox} + x_{64\purplebox} + x_{65\purplebox} + x_{66\purplebox} = 2 x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 2 Purple Patch x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 6 x_{11\greenbox} + x_{12\greenbox} + x_{13\greenbox} + x_{14\greenbox} + x_{15\greenbox} + x_{16\greenbox} + x_{21\greenbox} + x_{22\greenbox} + x_{23\greenbox} + x_{24\greenbox} + x_{25\greenbox} + x_{26\greenbox} + x_{31\greenbox} + x_{32\greenbox} + x_{33\greenbox} + x_{34\greenbox} + x_{35\greenbox} + x_{36\greenbox} + x_{41\greenbox} + x_{42\greenbox} + x_{43\greenbox} + x_{44\greenbox} + x_{45\greenbox} + x_{46\greenbox} + x_{51\greenbox} + x_{52\greenbox} + x_{53\greenbox} + x_{54\greenbox} + x_{55\greenbox} + x_{56\greenbox} + x_{61\greenbox} + x_{62\greenbox} + x_{63\greenbox} + x_{64\greenbox} + x_{65\greenbox} + x_{66\greenbox} = 6 x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 6 Green Patch x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 2 x_{11\orangebox} + x_{12\orangebox} + x_{13\orangebox} + x_{14\orangebox} + x_{15\orangebox} + x_{16\orangebox} + x_{21\orangebox} + x_{22\orangebox} + x_{23\orangebox} + x_{24\orangebox} + x_{25\orangebox} + x_{26\orangebox} + x_{31\orangebox} + x_{32\orangebox} + x_{33\orangebox} + x_{34\orangebox} + x_{35\orangebox} + x_{36\orangebox} + x_{41\orangebox} + x_{42\orangebox} + x_{43\orangebox} + x_{44\orangebox} + x_{45\orangebox} + x_{46\orangebox} + x_{51\orangebox} + x_{52\orangebox} + x_{53\orangebox} + x_{54\orangebox} + x_{55\orangebox} + x_{56\orangebox} + x_{61\orangebox} + x_{62\orangebox} + x_{63\orangebox} + x_{64\orangebox} + x_{65\orangebox} + x_{66\orangebox} = 2 x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 2 Orange Patch x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 4 x_{11\redbox} + x_{12\redbox} + x_{13\redbox} + x_{14\redbox} + x_{15\redbox} + x_{16\redbox} + x_{21\redbox} + x_{22\redbox} + x_{23\redbox} + x_{24\redbox} + x_{25\redbox} + x_{26\redbox} + x_{31\redbox} + x_{32\redbox} + x_{33\redbox} + x_{34\redbox} + x_{35\redbox} + x_{36\redbox} + x_{41\redbox} + x_{42\redbox} + x_{43\redbox} + x_{44\redbox} + x_{45\redbox} + x_{46\redbox} + x_{51\redbox} + x_{52\redbox} + x_{53\redbox} + x_{54\redbox} + x_{55\redbox} + x_{56\redbox} + x_{61\redbox} + x_{62\redbox} + x_{63\redbox} + x_{64\redbox} + x_{65\redbox} + x_{66\redbox} = 4 x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 4 Red Patch x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 2 x_{11\bluebox} + x_{12\bluebox} + x_{13\bluebox} + x_{14\bluebox} + x_{15\bluebox} + x_{16\bluebox} + x_{21\bluebox} + x_{22\bluebox} + x_{23\bluebox} + x_{24\bluebox} + x_{25\bluebox}+ x_{26\bluebox} + x_{31\bluebox} + x_{32\bluebox} + x_{33\bluebox} + x_{34\bluebox} + x_{35\bluebox} + x_{36\bluebox} + x_{41\bluebox} + x_{42\bluebox} + x_{43\bluebox} + x_{44\bluebox} +x_{45\bluebox} + x_{46\bluebox} + x_{51\bluebox} + x_{52\bluebox} + x_{53\bluebox} + x_{54\bluebox} + x_{55\bluebox} + x_{56\bluebox} + x_{61\bluebox} + x_{62\bluebox} + x_{63\bluebox} + x_{64\bluebox} + x_{65\bluebox} + x_{66\bluebox} = 2 x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 2 Blue Patch x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 2 x_{11\magentabox} + x_{12\magentabox} + x_{13\magentabox} + x_{14\magentabox} + x_{15\magentabox} + x_{16\magentabox} + x_{21\magentabox} + x_{22\magentabox} + x_{23\magentabox} + x_{24\magentabox} + x_{25\magentabox} + x_{26\magentabox} + x_{31\magentabox} + x_{32\magentabox} + x_{33\magentabox} + x_{34\magentabox} + x_{35\magentabox} + x_{36\magentabox} + x_{41\magentabox} + x_{42\magentabox} + x_{43\magentabox} + x_{44\magentabox} + x_{45\magentabox} + x_{46\magentabox} + x_{51\magentabox} + x_{52\magentabox} + x_{53\magentabox} + x_{54\magentabox} + x_{55\magentabox} + x_{56\magentabox} + x_{61\magentabox} + x_{62\magentabox} + x_{63\magentabox} + x_{64\magentabox} + x_{65\magentabox} + x_{66\magentabox} = 2 x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 2 Magenta Patch x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 6 x_{11\brickbox} + x_{12\brickbox} + x_{13\brickbox} + x_{14\brickbox} + x_{15\brickbox} + x_{16\brickbox} + x_{21\brickbox} + x_{22\brickbox} + x_{23\brickbox} + x_{24\brickbox} + x_{25\brickbox} + x_{26\brickbox} + x_{31\brickbox} + x_{32\brickbox} + x_{33\brickbox} + x_{34\brickbox} + x_{35\brickbox} + x_{36\brickbox} + x_{41\brickbox} + x_{42\brickbox} + x_{43\brickbox} + x_{44\brickbox} + x_{45\brickbox} + x_{46\brickbox} + x_{51\brickbox} + x_{52\brickbox} + x_{53\brickbox} + x_{54\brickbox} + x_{55\brickbox} + x_{56\brickbox} + x_{61\brickbox} + x_{62\brickbox} + x_{63\brickbox} + x_{64\brickbox} + x_{65\brickbox} + x_{66\brickbox} = 6 x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 6 Brick Patch x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 4 x_{11\brownbox} + x_{12\brownbox} + x_{13\brownbox} + x_{14\brownbox} + x_{15\brownbox} + x_{16\brownbox} + x_{21\brownbox} + x_{22\brownbox} + x_{23\brownbox} + x_{24\brownbox} + x_{25\brownbox} + x_{26\brownbox} + x_{31\brownbox} + x_{32\brownbox} + x_{33\brownbox} + x_{34\brownbox} + x_{35\brownbox} + x_{36\brownbox} + x_{41\brownbox} + x_{42\brownbox} + x_{43\brownbox} + x_{44\brownbox} + x_{45\brownbox} + x_{46\brownbox} + x_{51\brownbox} + x_{52\brownbox} + x_{53\brownbox} + x_{54\brownbox} + x_{55\brownbox} + x_{56\brownbox} + x_{61\brownbox} + x_{62\brownbox} + x_{63\brownbox} + x_{64\brownbox} + x_{65\brownbox} + x_{66\brownbox} = 4 x 11 ■ + x 12 ■ + x 13 ■ + x 14 ■ + x 15 ■ + x 16 ■ + x 21 ■ + x 22 ■ + x 23 ■ + x 24 ■ + x 25 ■ + x 26 ■ + x 31 ■ + x 32 ■ + x 33 ■ + x 34 ■ + x 35 ■ + x 36 ■ + x 41 ■ + x 42 ■ + x 43 ■ + x 44 ■ + x 45 ■ + x 46 ■ + x 51 ■ + x 52 ■ + x 53 ■ + x 54 ■ + x 55 ■ + x 56 ■ + x 61 ■ + x 62 ■ + x 63 ■ + x 64 ■ + x 65 ■ + x 66 ■ = 4 Brown Patch Vertical-Patch Constraints w ■ < h ■ w_{\orangebox} < h_{\orangebox} w ■ < h ■ Orange Patch Square-Patch Constraints w ■ = h ■ w_{\redbox} = h_{\redbox} w ■ = h ■ Red Patch Integrity Constraints l ■ ∈ N l_{\yellowbox} \in \N l ■ ∈ N Yellow Patch l ■ ∈ N l_{\tealbox} \in \N l ■ ∈ N Teal Patch l ■ ∈ N l_{\purplebox} \in \N l ■ ∈ N Purple Patch l ■ ∈ N l_{\greenbox} \in \N l ■ ∈ N Green Patch l ■ ∈ N l_{\orangebox} \in \N l ■ ∈ N Orange Patch l ■ ∈ N l_{\redbox} \in \N l ■ ∈ N Red Patch l ■ ∈ N l_{\bluebox} \in \N l ■ ∈ N Blue Patch l ■ ∈ N l_{\magentabox} \in \N l ■ ∈ N Magenta Patch l ■ ∈ N l_{\brickbox} \in \N l ■ ∈ N Brick Patch l ■ ∈ N l_{\brownbox} \in \N l ■ ∈ N Brown Patch w ■ ∈ N w_{\yellowbox} \in \N w ■ ∈ N Yellow Patch w ■ ∈ N w_{\tealbox} \in \N w ■ ∈ N Teal Patch w ■ ∈ N w_{\purplebox} \in \N w ■ ∈ N Purple Patch w ■ ∈ N w_{\greenbox} \in \N w ■ ∈ N Green Patch w ■ ∈ N w_{\orangebox} \in \N w ■ ∈ N Orange Patch w ■ ∈ N w_{\redbox} \in \N w ■ ∈ N Red Patch w ■ ∈ N w_{\bluebox} \in \N w ■ ∈ N Blue Patch w ■ ∈ N w_{\magentabox} \in \N w ■ ∈ N Magenta Patch w ■ ∈ N w_{\brickbox} \in \N w ■ ∈ N Brick Patch w ■ ∈ N w_{\brownbox} \in \N w ■ ∈ N Brown Patch t ■ ∈ N t_{\yellowbox} \in \N t ■ ∈ N Yellow Patch t ■ ∈ N t_{\tealbox} \in \N t ■ ∈ N Teal Patch t ■ ∈ N t_{\purplebox} \in \N t ■ ∈ N Purple Patch t ■ ∈ N t_{\greenbox} \in \N t ■ ∈ N Green Patch t ■ ∈ N t_{\orangebox} \in \N t ■ ∈ N Orange Patch t ■ ∈ N t_{\redbox} \in \N t ■ ∈ N Red Patch t ■ ∈ N t_{\bluebox} \in \N t ■ ∈ N Blue Patch t ■ ∈ N t_{\magentabox} \in \N t ■ ∈ N Magenta Patch t ■ ∈ N t_{\brickbox} \in \N t ■ ∈ N Brick Patch t ■ ∈ N t_{\brownbox} \in \N t ■ ∈ N Brown Patch h ■ ∈ N h_{\yellowbox} \in \N h ■ ∈ N Yellow Patch h ■ ∈ N h_{\tealbox} \in \N h ■ ∈ N Teal Patch h ■ ∈ N h_{\purplebox} \in \N h ■ ∈ N Purple Patch h ■ ∈ N h_{\greenbox} \in \N h ■ ∈ N Green Patch h ■ ∈ N h_{\orangebox} \in \N h ■ ∈ N Orange Patch h ■ ∈ N h_{\redbox} \in \N h ■ ∈ N Red Patch h ■ ∈ N h_{\bluebox} \in \N h ■ ∈ N Blue Patch h ■ ∈ N h_{\magentabox} \in \N h ■ ∈ N Magenta Patch h ■ ∈ N h_{\brickbox} \in \N h ■ ∈ N Brick Patch h ■ ∈ N h_{\brownbox} \in \N h ■ ∈ N Brown Patch Binarity Constraints u 1 ■ ∈ { 0 , 1 } u_{1\yellowbox} \in \B u 1 ■ ∈ { 0 , 1 } Row 1, Yellow Patch u 2 ■ ∈ { 0 , 1 } u_{2\yellowbox} \in \B u 2 ■ ∈ { 0 , 1 } Row 2, Yellow Patch u 3 ■ ∈ { 0 , 1 } u_{3\yellowbox} \in \B u 3 ■ ∈ { 0 , 1 } Row 3, Yellow Patch u 4 ■ ∈ { 0 , 1 } u_{4\yellowbox} \in \B u 4 ■ ∈ { 0 , 1 } Row 4, Yellow Patch u 5 ■ ∈ { 0 , 1 } u_{5\yellowbox} \in \B u 5 ■ ∈ { 0 , 1 } Row 5, Yellow Patch u 6 ■ ∈ { 0 , 1 } u_{6\yellowbox} \in \B u 6 ■ ∈ { 0 , 1 } Row 6, Yellow Patch u 1 ■ ∈ { 0 , 1 } u_{1\tealbox} \in \B u 1 ■ ∈ { 0 , 1 } Row 1, Tealbox Patch u 2 ■ ∈ { 0 , 1 } u_{2\tealbox} \in \B u 2 ■ ∈ { 0 , 1 } Row 2, Tealbox Patch u 3 ■ ∈ { 0 , 1 } u_{3\tealbox} \in \B u 3 ■ ∈ { 0 , 1 } Row 3, Tealbox Patch u 4 ■ ∈ { 0 , 1 } u_{4\tealbox} \in \B u 4 ■ ∈ { 0 , 1 } Row 4, Tealbox Patch u 5 ■ ∈ { 0 , 1 } u_{5\tealbox} \in \B u 5 ■ ∈ { 0 , 1 } Row 5, Tealbox Patch u 6 ■ ∈ { 0 , 1 } u_{6\tealbox} \in \B u 6 ■ ∈ { 0 , 1 } Row 6, Tealbox Patch u 1 ■ ∈ { 0 , 1 } u_{1\purplebox} \in \B u 1 ■ ∈ { 0 , 1 } Row 1, Purple Patch u 2 ■ ∈ { 0 , 1 } u_{2\purplebox} \in \B u 2 ■ ∈ { 0 , 1 } Row 2, Purple Patch u 3 ■ ∈ { 0 , 1 } u_{3\purplebox} \in \B u 3 ■ ∈ { 0 , 1 } Row 3, Purple Patch u 4 ■ ∈ { 0 , 1 } u_{4\purplebox} \in \B u 4 ■ ∈ { 0 , 1 } Row 4, Purple Patch u 5 ■ ∈ { 0 , 1 } u_{5\purplebox} \in \B u 5 ■ ∈ { 0 , 1 } Row 5, Purple Patch u 6 ■ ∈ { 0 , 1 } u_{6\purplebox} \in \B u 6 ■ ∈ { 0 , 1 } Row 6, Purple Patch u 1 ■ ∈ { 0 , 1 } u_{1\greenbox} \in \B u 1 ■ ∈ { 0 , 1 } Row 1, Green Patch u 2 ■ ∈ { 0 , 1 } u_{2\greenbox} \in \B u 2 ■ ∈ { 0 , 1 } Row 2, Green Patch u 3 ■ ∈ { 0 , 1 } u_{3\greenbox} \in \B u 3 ■ ∈ { 0 , 1 } Row 3, Green Patch u 4 ■ ∈ { 0 , 1 } u_{4\greenbox} \in \B u 4 ■ ∈ { 0 , 1 } Row 4, Green Patch u 5 ■ ∈ { 0 , 1 } u_{5\greenbox} \in \B u 5 ■ ∈ { 0 , 1 } Row 5, Green Patch u 6 ■ ∈ { 0 , 1 } u_{6\greenbox} \in \B u 6 ■ ∈ { 0 , 1 } Row 6, Green Patch u 1 ■ ∈ { 0 , 1 } u_{1\orangebox} \in \B u 1 ■ ∈ { 0 , 1 } Row 1, Orange Patch u 2 ■ ∈ { 0 , 1 } u_{2\orangebox} \in \B u 2 ■ ∈ { 0 , 1 } Row 2, Orange Patch u 3 ■ ∈ { 0 , 1 } u_{3\orangebox} \in \B u 3 ■ ∈ { 0 , 1 } Row 3, Orange Patch u 4 ■ ∈ { 0 , 1 } u_{4\orangebox} \in \B u 4 ■ ∈ { 0 , 1 } Row 4, Orange Patch u 5 ■ ∈ { 0 , 1 } u_{5\orangebox} \in \B u 5 ■ ∈ { 0 , 1 } Row 5, Orange Patch u 6 ■ ∈ { 0 , 1 } u_{6\orangebox} \in \B u 6 ■ ∈ { 0 , 1 } Row 6, Orange Patch u 1 ■ ∈ { 0 , 1 } u_{1\redbox} \in \B u 1 ■ ∈ { 0 , 1 } Row 1, Red Patch u 2 ■ ∈ { 0 , 1 } u_{2\redbox} \in \B u 2 ■ ∈ { 0 , 1 } Row 2, Red Patch u 3 ■ ∈ { 0 , 1 } u_{3\redbox} \in \B u 3 ■ ∈ { 0 , 1 } Row 3, Red Patch u 4 ■ ∈ { 0 , 1 } u_{4\redbox} \in \B u 4 ■ ∈ { 0 , 1 } Row 4, Red Patch u 5 ■ ∈ { 0 , 1 } u_{5\redbox} \in \B u 5 ■ ∈ { 0 , 1 } Row 5, Red Patch u 6 ■ ∈ { 0 , 1 } u_{6\redbox} \in \B u 6 ■ ∈ { 0 , 1 } Row 6, Red Patch u 1 ■ ∈ { 0 , 1 } u_{1\bluebox} \in \B u 1 ■ ∈ { 0 , 1 } Row 1, Blue Patch u 2 ■ ∈ { 0 , 1 } u_{2\bluebox} \in \B u 2 ■ ∈ { 0 , 1 } Row 2, Blue Patch u 3 ■ ∈ { 0 , 1 } u_{3\bluebox} \in \B u 3 ■ ∈ { 0 , 1 } Row 3, Blue Patch u 4 ■ ∈ { 0 , 1 } u_{4\bluebox} \in \B u 4 ■ ∈ { 0 , 1 } Row 4, Blue Patch u 5 ■ ∈ { 0 , 1 } u_{5\bluebox} \in \B u 5 ■ ∈ { 0 , 1 } Row 5, Blue Patch u 6 ■ ∈ { 0 , 1 } u_{6\bluebox} \in \B u 6 ■ ∈ { 0 , 1 } Row 6, Blue Patch u 1 ■ ∈ { 0 , 1 } u_{1\magentabox} \in \B u 1 ■ ∈ { 0 , 1 } Row 1, Magenta Patch u 2 ■ ∈ { 0 , 1 } u_{2\magentabox} \in \B u 2 ■ ∈ { 0 , 1 } Row 2, Magenta Patch u 3 ■ ∈ { 0 , 1 } u_{3\magentabox} \in \B u 3 ■ ∈ { 0 , 1 } Row 3, Magenta Patch u 4 ■ ∈ { 0 , 1 } u_{4\magentabox} \in \B u 4 ■ ∈ { 0 , 1 } Row 4, Magenta Patch u 5 ■ ∈ { 0 , 1 } u_{5\magentabox} \in \B u 5 ■ ∈ { 0 , 1 } Row 5, Magenta Patch u 6 ■ ∈ { 0 , 1 } u_{6\magentabox} \in \B u 6 ■ ∈ { 0 , 1 } Row 6, Magenta Patch u 1 ■ ∈ { 0 , 1 } u_{1\brickbox} \in \B u 1 ■ ∈ { 0 , 1 } Row 1, Brick Patch u 2 ■ ∈ { 0 , 1 } u_{2\brickbox} \in \B u 2 ■ ∈ { 0 , 1 } Row 2, Brick Patch u 3 ■ ∈ { 0 , 1 } u_{3\brickbox} \in \B u 3 ■ ∈ { 0 , 1 } Row 3, Brick Patch u 4 ■ ∈ { 0 , 1 } u_{4\brickbox} \in \B u 4 ■ ∈ { 0 , 1 } Row 4, Brick Patch u 5 ■ ∈ { 0 , 1 } u_{5\brickbox} \in \B u 5 ■ ∈ { 0 , 1 } Row 5, Brick Patch u 6 ■ ∈ { 0 , 1 } u_{6\brickbox} \in \B u 6 ■ ∈ { 0 , 1 } Row 6, Brick Patch u 1 ■ ∈ { 0 , 1 } u_{1\brownbox} \in \B u 1 ■ ∈ { 0 , 1 } Row 1, Brown Patch u 2 ■ ∈ { 0 , 1 } u_{2\brownbox} \in \B u 2 ■ ∈ { 0 , 1 } Row 2, Brown Patch u 3 ■ ∈ { 0 , 1 } u_{3\brownbox} \in \B u 3 ■ ∈ { 0 , 1 } Row 3, Brown Patch u 4 ■ ∈ { 0 , 1 } u_{4\brownbox} \in \B u 4 ■ ∈ { 0 , 1 } Row 4, Brown Patch u 5 ■ ∈ { 0 , 1 } u_{5\brownbox} \in \B u 5 ■ ∈ { 0 , 1 } Row 5, Brown Patch u 6 ■ ∈ { 0 , 1 } u_{6\brownbox} \in \B u 6 ■ ∈ { 0 , 1 } Row 6, Brown Patch v 1 ■ ∈ { 0 , 1 } v_{1\yellowbox} \in \B v 1 ■ ∈ { 0 , 1 } Column 1, Yellow Patch v 2 ■ ∈ { 0 , 1 } v_{2\yellowbox} \in \B v 2 ■ ∈ { 0 , 1 } Column 2, Yellow Patch v 3 ■ ∈ { 0 , 1 } v_{3\yellowbox} \in \B v 3 ■ ∈ { 0 , 1 } Column 3, Yellow Patch v 4 ■ ∈ { 0 , 1 } v_{4\yellowbox} \in \B v 4 ■ ∈ { 0 , 1 } Column 4, Yellow Patch v 5 ■ ∈ { 0 , 1 } v_{5\yellowbox} \in \B v 5 ■ ∈ { 0 , 1 } Column 5, Yellow Patch v 6 ■ ∈ { 0 , 1 } v_{6\yellowbox} \in \B v 6 ■ ∈ { 0 , 1 } Column 6, Yellow Patch v 1 ■ ∈ { 0 , 1 } v_{1\tealbox} \in \B v 1 ■ ∈ { 0 , 1 } Column 1, Tealbox Patch v 2 ■ ∈ { 0 , 1 } v_{2\tealbox} \in \B v 2 ■ ∈ { 0 , 1 } Column 2, Tealbox Patch v 3 ■ ∈ { 0 , 1 } v_{3\tealbox} \in \B v 3 ■ ∈ { 0 , 1 } Column 3, Tealbox Patch v 4 ■ ∈ { 0 , 1 } v_{4\tealbox} \in \B v 4 ■ ∈ { 0 , 1 } Column 4, Tealbox Patch v 5 ■ ∈ { 0 , 1 } v_{5\tealbox} \in \B v 5 ■ ∈ { 0 , 1 } Column 5, Tealbox Patch v 6 ■ ∈ { 0 , 1 } v_{6\tealbox} \in \B v 6 ■ ∈ { 0 , 1 } Column 6, Tealbox Patch v 1 ■ ∈ { 0 , 1 } v_{1\purplebox} \in \B v 1 ■ ∈ { 0 , 1 } Column 1, Purple Patch v 2 ■ ∈ { 0 , 1 } v_{2\purplebox} \in \B v 2 ■ ∈ { 0 , 1 } Column 2, Purple Patch v 3 ■ ∈ { 0 , 1 } v_{3\purplebox} \in \B v 3 ■ ∈ { 0 , 1 } Column 3, Purple Patch v 4 ■ ∈ { 0 , 1 } v_{4\purplebox} \in \B v 4 ■ ∈ { 0 , 1 } Column 4, Purple Patch v 5 ■ ∈ { 0 , 1 } v_{5\purplebox} \in \B v 5 ■ ∈ { 0 , 1 } Column 5, Purple Patch v 6 ■ ∈ { 0 , 1 } v_{6\purplebox} \in \B v 6 ■ ∈ { 0 , 1 } Column 6, Purple Patch v 1 ■ ∈ { 0 , 1 } v_{1\greenbox} \in \B v 1 ■ ∈ { 0 , 1 } Column 1, Green Patch v 2 ■ ∈ { 0 , 1 } v_{2\greenbox} \in \B v 2 ■ ∈ { 0 , 1 } Column 2, Green Patch v 3 ■ ∈ { 0 , 1 } v_{3\greenbox} \in \B v 3 ■ ∈ { 0 , 1 } Column 3, Green Patch v 4 ■ ∈ { 0 , 1 } v_{4\greenbox} \in \B v 4 ■ ∈ { 0 , 1 } Column 4, Green Patch v 5 ■ ∈ { 0 , 1 } v_{5\greenbox} \in \B v 5 ■ ∈ { 0 , 1 } Column 5, Green Patch v 6 ■ ∈ { 0 , 1 } v_{6\greenbox} \in \B v 6 ■ ∈ { 0 , 1 } Column 6, Green Patch v 1 ■ ∈ { 0 , 1 } v_{1\orangebox} \in \B v 1 ■ ∈ { 0 , 1 } Column 1, Orange Patch v 2 ■ ∈ { 0 , 1 } v_{2\orangebox} \in \B v 2 ■ ∈ { 0 , 1 } Column 2, Orange Patch v 3 ■ ∈ { 0 , 1 } v_{3\orangebox} \in \B v 3 ■ ∈ { 0 , 1 } Column 3, Orange Patch v 4 ■ ∈ { 0 , 1 } v_{4\orangebox} \in \B v 4 ■ ∈ { 0 , 1 } Column 4, Orange Patch v 5 ■ ∈ { 0 , 1 } v_{5\orangebox} \in \B v 5 ■ ∈ { 0 , 1 } Column 5, Orange Patch v 6 ■ ∈ { 0 , 1 } v_{6\orangebox} \in \B v 6 ■ ∈ { 0 , 1 } Column 6, Orange Patch v 1 ■ ∈ { 0 , 1 } v_{1\redbox} \in \B v 1 ■ ∈ { 0 , 1 } Column 1, Red Patch v 2 ■ ∈ { 0 , 1 } v_{2\redbox} \in \B v 2 ■ ∈ { 0 , 1 } Column 2, Red Patch v 3 ■ ∈ { 0 , 1 } v_{3\redbox} \in \B v 3 ■ ∈ { 0 , 1 } Column 3, Red Patch v 4 ■ ∈ { 0 , 1 } v_{4\redbox} \in \B v 4 ■ ∈ { 0 , 1 } Column 4, Red Patch v 5 ■ ∈ { 0 , 1 } v_{5\redbox} \in \B v 5 ■ ∈ { 0 , 1 } Column 5, Red Patch v 6 ■ ∈ { 0 , 1 } v_{6\redbox} \in \B v 6 ■ ∈ { 0 , 1 } Column 6, Red Patch v 1 ■ ∈ { 0 , 1 } v_{1\bluebox} \in \B v 1 ■ ∈ { 0 , 1 } Column 1, Blue Patch v 2 ■ ∈ { 0 , 1 } v_{2\bluebox} \in \B v 2 ■ ∈ { 0 , 1 } Column 2, Blue Patch v 3 ■ ∈ { 0 , 1 } v_{3\bluebox} \in \B v 3 ■ ∈ { 0 , 1 } Column 3, Blue Patch v 4 ■ ∈ { 0 , 1 } v_{4\bluebox} \in \B v 4 ■ ∈ { 0 , 1 } Column 4, Blue Patch v 5 ■ ∈ { 0 , 1 } v_{5\bluebox} \in \B v 5 ■ ∈ { 0 , 1 } Column 5, Blue Patch v 6 ■ ∈ { 0 , 1 } v_{6\bluebox} \in \B v 6 ■ ∈ { 0 , 1 } Column 6, Blue Patch v 1 ■ ∈ { 0 , 1 } v_{1\magentabox} \in \B v 1 ■ ∈ { 0 , 1 } Column 1, Magenta Patch v 2 ■ ∈ { 0 , 1 } v_{2\magentabox} \in \B v 2 ■ ∈ { 0 , 1 } Column 2, Magenta Patch v 3 ■ ∈ { 0 , 1 } v_{3\magentabox} \in \B v 3 ■ ∈ { 0 , 1 } Column 3, Magenta Patch v 4 ■ ∈ { 0 , 1 } v_{4\magentabox} \in \B v 4 ■ ∈ { 0 , 1 } Column 4, Magenta Patch v 5 ■ ∈ { 0 , 1 } v_{5\magentabox} \in \B v 5 ■ ∈ { 0 , 1 } Column 5, Magenta Patch v 6 ■ ∈ { 0 , 1 } v_{6\magentabox} \in \B v 6 ■ ∈ { 0 , 1 } Column 6, Magenta Patch v 1 ■ ∈ { 0 , 1 } v_{1\brickbox} \in \B v 1 ■ ∈ { 0 , 1 } Column 1, Brick Patch v 2 ■ ∈ { 0 , 1 } v_{2\brickbox} \in \B v 2 ■ ∈ { 0 , 1 } Column 2, Brick Patch v 3 ■ ∈ { 0 , 1 } v_{3\brickbox} \in \B v 3 ■ ∈ { 0 , 1 } Column 3, Brick Patch v 4 ■ ∈ { 0 , 1 } v_{4\brickbox} \in \B v 4 ■ ∈ { 0 , 1 } Column 4, Brick Patch v 5 ■ ∈ { 0 , 1 } v_{5\brickbox} \in \B v 5 ■ ∈ { 0 , 1 } Column 5, Brick Patch v 6 ■ ∈ { 0 , 1 } v_{6\brickbox} \in \B v 6 ■ ∈ { 0 , 1 } Column 6, Brick Patch v 1 ■ ∈ { 0 , 1 } v_{1\brownbox} \in \B v 1 ■ ∈ { 0 , 1 } Column 1, Brown Patch v 2 ■ ∈ { 0 , 1 } v_{2\brownbox} \in \B v 2 ■ ∈ { 0 , 1 } Column 2, Brown Patch v 3 ■ ∈ { 0 , 1 } v_{3\brownbox} \in \B v 3 ■ ∈ { 0 , 1 } Column 3, Brown Patch v 4 ■ ∈ { 0 , 1 } v_{4\brownbox} \in \B v 4 ■ ∈ { 0 , 1 } Column 4, Brown Patch v 5 ■ ∈ { 0 , 1 } v_{5\brownbox} \in \B v 5 ■ ∈ { 0 , 1 } Column 5, Brown Patch v 6 ■ ∈ { 0 , 1 } v_{6\brownbox} \in \B v 6 ■ ∈ { 0 , 1 } Column 6, Brown Patch x 11 ■ ∈ { 0 , 1 } x_{11\yellowbox} \in \B x 11 ■ ∈ { 0 , 1 } Square (1,1), Yellow Patch x 12 ■ ∈ { 0 , 1 } x_{12\yellowbox} \in \B x 12 ■ ∈ { 0 , 1 } Square (1,2), Yellow Patch x 13 ■ ∈ { 0 , 1 } x_{13\yellowbox} \in \B x 13 ■ ∈ { 0 , 1 } Square (1,3), Yellow Patch x 14 ■ ∈ { 0 , 1 } x_{14\yellowbox} \in \B x 14 ■ ∈ { 0 , 1 } Square (1,4), Yellow Patch x 15 ■ ∈ { 0 , 1 } x_{15\yellowbox} \in \B x 15 ■ ∈ { 0 , 1 } Square (1,5), Yellow Patch x 16 ■ ∈ { 0 , 1 } x_{16\yellowbox} \in \B x 16 ■ ∈ { 0 , 1 } Square (1,6), Yellow Patch x 21 ■ ∈ { 0 , 1 } x_{21\yellowbox} \in \B x 21 ■ ∈ { 0 , 1 } Square (2,1), Yellow Patch x 22 ■ ∈ { 0 , 1 } x_{22\yellowbox} \in \B x 22 ■ ∈ { 0 , 1 } Square (2,2), Yellow Patch x 23 ■ ∈ { 0 , 1 } x_{23\yellowbox} \in \B x 23 ■ ∈ { 0 , 1 } Square (2,3), Yellow Patch x 24 ■ ∈ { 0 , 1 } x_{24\yellowbox} \in \B x 24 ■ ∈ { 0 , 1 } Square (2,4), Yellow Patch x 25 ■ ∈ { 0 , 1 } x_{25\yellowbox} \in \B x 25 ■ ∈ { 0 , 1 } Square (2,5), Yellow Patch x 26 ■ ∈ { 0 , 1 } x_{26\yellowbox} \in \B x 26 ■ ∈ { 0 , 1 } Square (2,6), Yellow Patch x 31 ■ ∈ { 0 , 1 } x_{31\yellowbox} \in \B x 31 ■ ∈ { 0 , 1 } Square (3,1), Yellow Patch x 32 ■ ∈ { 0 , 1 } x_{32\yellowbox} \in \B x 32 ■ ∈ { 0 , 1 } Square (3,2), Yellow Patch x 33 ■ ∈ { 0 , 1 } x_{33\yellowbox} \in \B x 33 ■ ∈ { 0 , 1 } Square (3,3), Yellow Patch x 34 ■ ∈ { 0 , 1 } x_{34\yellowbox} \in \B x 34 ■ ∈ { 0 , 1 } Square (3,4), Yellow Patch x 35 ■ ∈ { 0 , 1 } x_{35\yellowbox} \in \B x 35 ■ ∈ { 0 , 1 } Square (3,5), Yellow Patch x 36 ■ ∈ { 0 , 1 } x_{36\yellowbox} \in \B x 36 ■ ∈ { 0 , 1 } Square (3,6), Yellow Patch x 41 ■ ∈ { 0 , 1 } x_{41\yellowbox} \in \B x 41 ■ ∈ { 0 , 1 } Square (4,1), Yellow Patch x 42 ■ ∈ { 0 , 1 } x_{42\yellowbox} \in \B x 42 ■ ∈ { 0 , 1 } Square (4,2), Yellow Patch x 43 ■ ∈ { 0 , 1 } x_{43\yellowbox} \in \B x 43 ■ ∈ { 0 , 1 } Square (4,3), Yellow Patch x 44 ■ ∈ { 0 , 1 } x_{44\yellowbox} \in \B x 44 ■ ∈ { 0 , 1 } Square (4,4), Yellow Patch x 45 ■ ∈ { 0 , 1 } x_{45\yellowbox} \in \B x 45 ■ ∈ { 0 , 1 } Square (4,5), Yellow Patch x 46 ■ ∈ { 0 , 1 } x_{46\yellowbox} \in \B x 46 ■ ∈ { 0 , 1 } Square (4,6), Yellow Patch x 51 ■ ∈ { 0 , 1 } x_{51\yellowbox} \in \B x 51 ■ ∈ { 0 , 1 } Square (5,1), Yellow Patch x 52 ■ ∈ { 0 , 1 } x_{52\yellowbox} \in \B x 52 ■ ∈ { 0 , 1 } Square (5,2), Yellow Patch x 53 ■ ∈ { 0 , 1 } x_{53\yellowbox} \in \B x 53 ■ ∈ { 0 , 1 } Square (5,3), Yellow Patch x 54 ■ ∈ { 0 , 1 } x_{54\yellowbox} \in \B x 54 ■ ∈ { 0 , 1 } Square (5,4), Yellow Patch x 55 ■ ∈ { 0 , 1 } x_{55\yellowbox} \in \B x 55 ■ ∈ { 0 , 1 } Square (5,5), Yellow Patch x 56 ■ ∈ { 0 , 1 } x_{56\yellowbox} \in \B x 56 ■ ∈ { 0 , 1 } Square (5,6), Yellow Patch x 61 ■ ∈ { 0 , 1 } x_{61\yellowbox} \in \B x 61 ■ ∈ { 0 , 1 } Square (6,1), Yellow Patch x 62 ■ ∈ { 0 , 1 } x_{62\yellowbox} \in \B x 62 ■ ∈ { 0 , 1 } Square (6,2), Yellow Patch x 63 ■ ∈ { 0 , 1 } x_{63\yellowbox} \in \B x 63 ■ ∈ { 0 , 1 } Square (6,3), Yellow Patch x 64 ■ ∈ { 0 , 1 } x_{64\yellowbox} \in \B x 64 ■ ∈ { 0 , 1 } Square (6,4), Yellow Patch x 65 ■ ∈ { 0 , 1 } x_{65\yellowbox} \in \B x 65 ■ ∈ { 0 , 1 } Square (6,5), Yellow Patch x 66 ■ ∈ { 0 , 1 } x_{66\yellowbox} \in \B x 66 ■ ∈ { 0 , 1 } Square (6,6), Yellow Patch x 11 ■ ∈ { 0 , 1 } x_{11\tealbox} \in \B x 11 ■ ∈ { 0 , 1 } Square (1,1), Teal x 12 ■ ∈ { 0 , 1 } x_{12\tealbox} \in \B x 12 ■ ∈ { 0 , 1 } Square (1,2), Teal x 13 ■ ∈ { 0 , 1 } x_{13\tealbox} \in \B x 13 ■ ∈ { 0 , 1 } Square (1,3), Teal x 14 ■ ∈ { 0 , 1 } x_{14\tealbox} \in \B x 14 ■ ∈ { 0 , 1 } Square (1,4), Teal x 15 ■ ∈ { 0 , 1 } x_{15\tealbox} \in \B x 15 ■ ∈ { 0 , 1 } Square (1,5), Teal x 16 ■ ∈ { 0 , 1 } x_{16\tealbox} \in \B x 16 ■ ∈ { 0 , 1 } Square (1,6), Teal x 21 ■ ∈ { 0 , 1 } x_{21\tealbox} \in \B x 21 ■ ∈ { 0 , 1 } Square (2,1), Teal x 22 ■ ∈ { 0 , 1 } x_{22\tealbox} \in \B x 22 ■ ∈ { 0 , 1 } Square (2,2), Teal x 23 ■ ∈ { 0 , 1 } x_{23\tealbox} \in \B x 23 ■ ∈ { 0 , 1 } Square (2,3), Teal x 24 ■ ∈ { 0 , 1 } x_{24\tealbox} \in \B x 24 ■ ∈ { 0 , 1 } Square (2,4), Teal x 25 ■ ∈ { 0 , 1 } x_{25\tealbox} \in \B x 25 ■ ∈ { 0 , 1 } Square (2,5), Teal x 26 ■ ∈ { 0 , 1 } x_{26\tealbox} \in \B x 26 ■ ∈ { 0 , 1 } Square (2,6), Teal x 31 ■ ∈ { 0 , 1 } x_{31\tealbox} \in \B x 31 ■ ∈ { 0 , 1 } Square (3,1), Teal x 32 ■ ∈ { 0 , 1 } x_{32\tealbox} \in \B x 32 ■ ∈ { 0 , 1 } Square (3,2), Teal x 33 ■ ∈ { 0 , 1 } x_{33\tealbox} \in \B x 33 ■ ∈ { 0 , 1 } Square (3,3), Teal x 34 ■ ∈ { 0 , 1 } x_{34\tealbox} \in \B x 34 ■ ∈ { 0 , 1 } Square (3,4), Teal x 35 ■ ∈ { 0 , 1 } x_{35\tealbox} \in \B x 35 ■ ∈ { 0 , 1 } Square (3,5), Teal x 36 ■ ∈ { 0 , 1 } x_{36\tealbox} \in \B x 36 ■ ∈ { 0 , 1 } Square (3,6), Teal x 41 ■ ∈ { 0 , 1 } x_{41\tealbox} \in \B x 41 ■ ∈ { 0 , 1 } Square (4,1), Teal x 42 ■ ∈ { 0 , 1 } x_{42\tealbox} \in \B x 42 ■ ∈ { 0 , 1 } Square (4,2), Teal x 43 ■ ∈ { 0 , 1 } x_{43\tealbox} \in \B x 43 ■ ∈ { 0 , 1 } Square (4,3), Teal x 44 ■ ∈ { 0 , 1 } x_{44\tealbox} \in \B x 44 ■ ∈ { 0 , 1 } Square (4,4), Teal x 45 ■ ∈ { 0 , 1 } x_{45\tealbox} \in \B x 45 ■ ∈ { 0 , 1 } Square (4,5), Teal x 46 ■ ∈ { 0 , 1 } x_{46\tealbox} \in \B x 46 ■ ∈ { 0 , 1 } Square (4,6), Teal x 51 ■ ∈ { 0 , 1 } x_{51\tealbox} \in \B x 51 ■ ∈ { 0 , 1 } Square (5,1), Teal x 52 ■ ∈ { 0 , 1 } x_{52\tealbox} \in \B x 52 ■ ∈ { 0 , 1 } Square (5,2), Teal x 53 ■ ∈ { 0 , 1 } x_{53\tealbox} \in \B x 53 ■ ∈ { 0 , 1 } Square (5,3), Teal x 54 ■ ∈ { 0 , 1 } x_{54\tealbox} \in \B x 54 ■ ∈ { 0 , 1 } Square (5,4), Teal x 55 ■ ∈ { 0 , 1 } x_{55\tealbox} \in \B x 55 ■ ∈ { 0 , 1 } Square (5,5), Teal x 56 ■ ∈ { 0 , 1 } x_{56\tealbox} \in \B x 56 ■ ∈ { 0 , 1 } Square (5,6), Teal x 61 ■ ∈ { 0 , 1 } x_{61\tealbox} \in \B x 61 ■ ∈ { 0 , 1 } Square (6,1), Teal x 62 ■ ∈ { 0 , 1 } x_{62\tealbox} \in \B x 62 ■ ∈ { 0 , 1 } Square (6,2), Teal x 63 ■ ∈ { 0 , 1 } x_{63\tealbox} \in \B x 63 ■ ∈ { 0 , 1 } Square (6,3), Teal x 64 ■ ∈ { 0 , 1 } x_{64\tealbox} \in \B x 64 ■ ∈ { 0 , 1 } Square (6,4), Teal x 65 ■ ∈ { 0 , 1 } x_{65\tealbox} \in \B x 65 ■ ∈ { 0 , 1 } Square (6,5), Teal x 66 ■ ∈ { 0 , 1 } x_{66\tealbox} \in \B x 66 ■ ∈ { 0 , 1 } Square (6,6), Teal x 11 ■ ∈ { 0 , 1 } x_{11\purplebox} \in \B x 11 ■ ∈ { 0 , 1 } Square (1,1), Purple Patch x 12 ■ ∈ { 0 , 1 } x_{12\purplebox} \in \B x 12 ■ ∈ { 0 , 1 } Square (1,2), Purple Patch x 13 ■ ∈ { 0 , 1 } x_{13\purplebox} \in \B x 13 ■ ∈ { 0 , 1 } Square (1,3), Purple Patch x 14 ■ ∈ { 0 , 1 } x_{14\purplebox} \in \B x 14 ■ ∈ { 0 , 1 } Square (1,4), Purple Patch x 15 ■ ∈ { 0 , 1 } x_{15\purplebox} \in \B x 15 ■ ∈ { 0 , 1 } Square (1,5), Purple Patch x 16 ■ ∈ { 0 , 1 } x_{16\purplebox} \in \B x 16 ■ ∈ { 0 , 1 } Square (1,6), Purple Patch x 21 ■ ∈ { 0 , 1 } x_{21\purplebox} \in \B x 21 ■ ∈ { 0 , 1 } Square (2,1), Purple Patch x 22 ■ ∈ { 0 , 1 } x_{22\purplebox} \in \B x 22 ■ ∈ { 0 , 1 } Square (2,2), Purple Patch x 23 ■ ∈ { 0 , 1 } x_{23\purplebox} \in \B x 23 ■ ∈ { 0 , 1 } Square (2,3), Purple Patch x 24 ■ ∈ { 0 , 1 } x_{24\purplebox} \in \B x 24 ■ ∈ { 0 , 1 } Square (2,4), Purple Patch x 25 ■ ∈ { 0 , 1 } x_{25\purplebox} \in \B x 25 ■ ∈ { 0 , 1 } Square (2,5), Purple Patch x 26 ■ ∈ { 0 , 1 } x_{26\purplebox} \in \B x 26 ■ ∈ { 0 , 1 } Square (2,6), Purple Patch x 31 ■ ∈ { 0 , 1 } x_{31\purplebox} \in \B x 31 ■ ∈ { 0 , 1 } Square (3,1), Purple Patch x 32 ■ ∈ { 0 , 1 } x_{32\purplebox} \in \B x 32 ■ ∈ { 0 , 1 } Square (3,2), Purple Patch x 33 ■ ∈ { 0 , 1 } x_{33\purplebox} \in \B x 33 ■ ∈ { 0 , 1 } Square (3,3), Purple Patch x 34 ■ ∈ { 0 , 1 } x_{34\purplebox} \in \B x 34 ■ ∈ { 0 , 1 } Square (3,4), Purple Patch x 35 ■ ∈ { 0 , 1 } x_{35\purplebox} \in \B x 35 ■ ∈ { 0 , 1 } Square (3,5), Purple Patch x 36 ■ ∈ { 0 , 1 } x_{36\purplebox} \in \B x 36 ■ ∈ { 0 , 1 } Square (3,6), Purple Patch x 41 ■ ∈ { 0 , 1 } x_{41\purplebox} \in \B x 41 ■ ∈ { 0 , 1 } Square (4,1), Purple Patch x 42 ■ ∈ { 0 , 1 } x_{42\purplebox} \in \B x 42 ■ ∈ { 0 , 1 } Square (4,2), Purple Patch x 43 ■ ∈ { 0 , 1 } x_{43\purplebox} \in \B x 43 ■ ∈ { 0 , 1 } Square (4,3), Purple Patch x 44 ■ ∈ { 0 , 1 } x_{44\purplebox} \in \B x 44 ■ ∈ { 0 , 1 } Square (4,4), Purple Patch x 45 ■ ∈ { 0 , 1 } x_{45\purplebox} \in \B x 45 ■ ∈ { 0 , 1 } Square (4,5), Purple Patch x 46 ■ ∈ { 0 , 1 } x_{46\purplebox} \in \B x 46 ■ ∈ { 0 , 1 } Square (4,6), Purple Patch x 51 ■ ∈ { 0 , 1 } x_{51\purplebox} \in \B x 51 ■ ∈ { 0 , 1 } Square (5,1), Purple Patch x 52 ■ ∈ { 0 , 1 } x_{52\purplebox} \in \B x 52 ■ ∈ { 0 , 1 } Square (5,2), Purple Patch x 53 ■ ∈ { 0 , 1 } x_{53\purplebox} \in \B x 53 ■ ∈ { 0 , 1 } Square (5,3), Purple Patch x 54 ■ ∈ { 0 , 1 } x_{54\purplebox} \in \B x 54 ■ ∈ { 0 , 1 } Square (5,4), Purple Patch x 55 ■ ∈ { 0 , 1 } x_{55\purplebox} \in \B x 55 ■ ∈ { 0 , 1 } Square (5,5), Purple Patch x 56 ■ ∈ { 0 , 1 } x_{56\purplebox} \in \B x 56 ■ ∈ { 0 , 1 } Square (5,6), Purple Patch x 61 ■ ∈ { 0 , 1 } x_{61\purplebox} \in \B x 61 ■ ∈ { 0 , 1 } Square (6,1), Purple Patch x 62 ■ ∈ { 0 , 1 } x_{62\purplebox} \in \B x 62 ■ ∈ { 0 , 1 } Square (6,2), Purple Patch x 63 ■ ∈ { 0 , 1 } x_{63\purplebox} \in \B x 63 ■ ∈ { 0 , 1 } Square (6,3), Purple Patch x 64 ■ ∈ { 0 , 1 } x_{64\purplebox} \in \B x 64 ■ ∈ { 0 , 1 } Square (6,4), Purple Patch x 65 ■ ∈ { 0 , 1 } x_{65\purplebox} \in \B x 65 ■ ∈ { 0 , 1 } Square (6,5), Purple Patch x 66 ■ ∈ { 0 , 1 } x_{66\purplebox} \in \B x 66 ■ ∈ { 0 , 1 } Square (6,6), Purple Patch x 11 ■ ∈ { 0 , 1 } x_{11\greenbox} \in \B x 11 ■ ∈ { 0 , 1 } Square (1,1), Green Patch x 12 ■ ∈ { 0 , 1 } x_{12\greenbox} \in \B x 12 ■ ∈ { 0 , 1 } Square (1,2), Green Patch x 13 ■ ∈ { 0 , 1 } x_{13\greenbox} \in \B x 13 ■ ∈ { 0 , 1 } Square (1,3), Green Patch x 14 ■ ∈ { 0 , 1 } x_{14\greenbox} \in \B x 14 ■ ∈ { 0 , 1 } Square (1,4), Green Patch x 15 ■ ∈ { 0 , 1 } x_{15\greenbox} \in \B x 15 ■ ∈ { 0 , 1 } Square (1,5), Green Patch x 16 ■ ∈ { 0 , 1 } x_{16\greenbox} \in \B x 16 ■ ∈ { 0 , 1 } Square (1,6), Green Patch x 21 ■ ∈ { 0 , 1 } x_{21\greenbox} \in \B x 21 ■ ∈ { 0 , 1 } Square (2,1), Green Patch x 22 ■ ∈ { 0 , 1 } x_{22\greenbox} \in \B x 22 ■ ∈ { 0 , 1 } Square (2,2), Green Patch x 23 ■ ∈ { 0 , 1 } x_{23\greenbox} \in \B x 23 ■ ∈ { 0 , 1 } Square (2,3), Green Patch x 24 ■ ∈ { 0 , 1 } x_{24\greenbox} \in \B x 24 ■ ∈ { 0 , 1 } Square (2,4), Green Patch x 25 ■ ∈ { 0 , 1 } x_{25\greenbox} \in \B x 25 ■ ∈ { 0 , 1 } Square (2,5), Green Patch x 26 ■ ∈ { 0 , 1 } x_{26\greenbox} \in \B x 26 ■ ∈ { 0 , 1 } Square (2,6), Green Patch x 31 ■ ∈ { 0 , 1 } x_{31\greenbox} \in \B x 31 ■ ∈ { 0 , 1 } Square (3,1), Green Patch x 32 ■ ∈ { 0 , 1 } x_{32\greenbox} \in \B x 32 ■ ∈ { 0 , 1 } Square (3,2), Green Patch x 33 ■ ∈ { 0 , 1 } x_{33\greenbox} \in \B x 33 ■ ∈ { 0 , 1 } Square (3,3), Green Patch x 34 ■ ∈ { 0 , 1 } x_{34\greenbox} \in \B x 34 ■ ∈ { 0 , 1 } Square (3,4), Green Patch x 35 ■ ∈ { 0 , 1 } x_{35\greenbox} \in \B x 35 ■ ∈ { 0 , 1 } Square (3,5), Green Patch x 36 ■ ∈ { 0 , 1 } x_{36\greenbox} \in \B x 36 ■ ∈ { 0 , 1 } Square (3,6), Green Patch x 41 ■ ∈ { 0 , 1 } x_{41\greenbox} \in \B x 41 ■ ∈ { 0 , 1 } Square (4,1), Green Patch x 42 ■ ∈ { 0 , 1 } x_{42\greenbox} \in \B x 42 ■ ∈ { 0 , 1 } Square (4,2), Green Patch x 43 ■ ∈ { 0 , 1 } x_{43\greenbox} \in \B x 43 ■ ∈ { 0 , 1 } Square (4,3), Green Patch x 44 ■ ∈ { 0 , 1 } x_{44\greenbox} \in \B x 44 ■ ∈ { 0 , 1 } Square (4,4), Green Patch x 45 ■ ∈ { 0 , 1 } x_{45\greenbox} \in \B x 45 ■ ∈ { 0 , 1 } Square (4,5), Green Patch x 46 ■ ∈ { 0 , 1 } x_{46\greenbox} \in \B x 46 ■ ∈ { 0 , 1 } Square (4,6), Green Patch x 51 ■ ∈ { 0 , 1 } x_{51\greenbox} \in \B x 51 ■ ∈ { 0 , 1 } Square (5,1), Green Patch x 52 ■ ∈ { 0 , 1 } x_{52\greenbox} \in \B x 52 ■ ∈ { 0 , 1 } Square (5,2), Green Patch x 53 ■ ∈ { 0 , 1 } x_{53\greenbox} \in \B x 53 ■ ∈ { 0 , 1 } Square (5,3), Green Patch x 54 ■ ∈ { 0 , 1 } x_{54\greenbox} \in \B x 54 ■ ∈ { 0 , 1 } Square (5,4), Green Patch x 55 ■ ∈ { 0 , 1 } x_{55\greenbox} \in \B x 55 ■ ∈ { 0 , 1 } Square (5,5), Green Patch x 56 ■ ∈ { 0 , 1 } x_{56\greenbox} \in \B x 56 ■ ∈ { 0 , 1 } Square (5,6), Green Patch x 61 ■ ∈ { 0 , 1 } x_{61\greenbox} \in \B x 61 ■ ∈ { 0 , 1 } Square (6,1), Green Patch x 62 ■ ∈ { 0 , 1 } x_{62\greenbox} \in \B x 62 ■ ∈ { 0 , 1 } Square (6,2), Green Patch x 63 ■ ∈ { 0 , 1 } x_{63\greenbox} \in \B x 63 ■ ∈ { 0 , 1 } Square (6,3), Green Patch x 64 ■ ∈ { 0 , 1 } x_{64\greenbox} \in \B x 64 ■ ∈ { 0 , 1 } Square (6,4), Green Patch x 65 ■ ∈ { 0 , 1 } x_{65\greenbox} \in \B x 65 ■ ∈ { 0 , 1 } Square (6,5), Green Patch x 66 ■ ∈ { 0 , 1 } x_{66\greenbox} \in \B x 66 ■ ∈ { 0 , 1 } Square (6,6), Green Patch x 11 ■ ∈ { 0 , 1 } x_{11\orangebox} \in \B x 11 ■ ∈ { 0 , 1 } Square (1,1), Orange Patch x 12 ■ ∈ { 0 , 1 } x_{12\orangebox} \in \B x 12 ■ ∈ { 0 , 1 } Square (1,2), Orange Patch x 13 ■ ∈ { 0 , 1 } x_{13\orangebox} \in \B x 13 ■ ∈ { 0 , 1 } Square (1,3), Orange Patch x 14 ■ ∈ { 0 , 1 } x_{14\orangebox} \in \B x 14 ■ ∈ { 0 , 1 } Square (1,4), Orange Patch x 15 ■ ∈ { 0 , 1 } x_{15\orangebox} \in \B x 15 ■ ∈ { 0 , 1 } Square (1,5), Orange Patch x 16 ■ ∈ { 0 , 1 } x_{16\orangebox} \in \B x 16 ■ ∈ { 0 , 1 } Square (1,6), Orange Patch x 21 ■ ∈ { 0 , 1 } x_{21\orangebox} \in \B x 21 ■ ∈ { 0 , 1 } Square (2,1), Orange Patch x 22 ■ ∈ { 0 , 1 } x_{22\orangebox} \in \B x 22 ■ ∈ { 0 , 1 } Square (2,2), Orange Patch x 23 ■ ∈ { 0 , 1 } x_{23\orangebox} \in \B x 23 ■ ∈ { 0 , 1 } Square (2,3), Orange Patch x 24 ■ ∈ { 0 , 1 } x_{24\orangebox} \in \B x 24 ■ ∈ { 0 , 1 } Square (2,4), Orange Patch x 25 ■ ∈ { 0 , 1 } x_{25\orangebox} \in \B x 25 ■ ∈ { 0 , 1 } Square (2,5), Orange Patch x 26 ■ ∈ { 0 , 1 } x_{26\orangebox} \in \B x 26 ■ ∈ { 0 , 1 } Square (2,6), Orange Patch x 31 ■ ∈ { 0 , 1 } x_{31\orangebox} \in \B x 31 ■ ∈ { 0 , 1 } Square (3,1), Orange Patch x 32 ■ ∈ { 0 , 1 } x_{32\orangebox} \in \B x 32 ■ ∈ { 0 , 1 } Square (3,2), Orange Patch x 33 ■ ∈ { 0 , 1 } x_{33\orangebox} \in \B x 33 ■ ∈ { 0 , 1 } Square (3,3), Orange Patch x 34 ■ ∈ { 0 , 1 } x_{34\orangebox} \in \B x 34 ■ ∈ { 0 , 1 } Square (3,4), Orange Patch x 35 ■ ∈ { 0 , 1 } x_{35\orangebox} \in \B x 35 ■ ∈ { 0 , 1 } Square (3,5), Orange Patch x 36 ■ ∈ { 0 , 1 } x_{36\orangebox} \in \B x 36 ■ ∈ { 0 , 1 } Square (3,6), Orange Patch x 41 ■ ∈ { 0 , 1 } x_{41\orangebox} \in \B x 41 ■ ∈ { 0 , 1 } Square (4,1), Orange Patch x 42 ■ ∈ { 0 , 1 } x_{42\orangebox} \in \B x 42 ■ ∈ { 0 , 1 } Square (4,2), Orange Patch x 43 ■ ∈ { 0 , 1 } x_{43\orangebox} \in \B x 43 ■ ∈ { 0 , 1 } Square (4,3), Orange Patch x 44 ■ ∈ { 0 , 1 } x_{44\orangebox} \in \B x 44 ■ ∈ { 0 , 1 } Square (4,4), Orange Patch x 45 ■ ∈ { 0 , 1 } x_{45\orangebox} \in \B x 45 ■ ∈ { 0 , 1 } Square (4,5), Orange Patch x 46 ■ ∈ { 0 , 1 } x_{46\orangebox} \in \B x 46 ■ ∈ { 0 , 1 } Square (4,6), Orange Patch x 51 ■ ∈ { 0 , 1 } x_{51\orangebox} \in \B x 51 ■ ∈ { 0 , 1 } Square (5,1), Orange Patch x 52 ■ ∈ { 0 , 1 } x_{52\orangebox} \in \B x 52 ■ ∈ { 0 , 1 } Square (5,2), Orange Patch x 53 ■ ∈ { 0 , 1 } x_{53\orangebox} \in \B x 53 ■ ∈ { 0 , 1 } Square (5,3), Orange Patch x 54 ■ ∈ { 0 , 1 } x_{54\orangebox} \in \B x 54 ■ ∈ { 0 , 1 } Square (5,4), Orange Patch x 55 ■ ∈ { 0 , 1 } x_{55\orangebox} \in \B x 55 ■ ∈ { 0 , 1 } Square (5,5), Orange Patch x 56 ■ ∈ { 0 , 1 } x_{56\orangebox} \in \B x 56 ■ ∈ { 0 , 1 } Square (5,6), Orange Patch x 61 ■ ∈ { 0 , 1 } x_{61\orangebox} \in \B x 61 ■ ∈ { 0 , 1 } Square (6,1), Orange Patch x 62 ■ ∈ { 0 , 1 } x_{62\orangebox} \in \B x 62 ■ ∈ { 0 , 1 } Square (6,2), Orange Patch x 63 ■ ∈ { 0 , 1 } x_{63\orangebox} \in \B x 63 ■ ∈ { 0 , 1 } Square (6,3), Orange Patch x 64 ■ ∈ { 0 , 1 } x_{64\orangebox} \in \B x 64 ■ ∈ { 0 , 1 } Square (6,4), Orange Patch x 65 ■ ∈ { 0 , 1 } x_{65\orangebox} \in \B x 65 ■ ∈ { 0 , 1 } Square (6,5), Orange Patch x 66 ■ ∈ { 0 , 1 } x_{66\orangebox} \in \B x 66 ■ ∈ { 0 , 1 } Square (6,6), Orange Patch x 11 ■ ∈ { 0 , 1 } x_{11\redbox} \in \B x 11 ■ ∈ { 0 , 1 } Square (1,1), Red Patch x 12 ■ ∈ { 0 , 1 } x_{12\redbox} \in \B x 12 ■ ∈ { 0 , 1 } Square (1,2), Red Patch x 13 ■ ∈ { 0 , 1 } x_{13\redbox} \in \B x 13 ■ ∈ { 0 , 1 } Square (1,3), Red Patch x 14 ■ ∈ { 0 , 1 } x_{14\redbox} \in \B x 14 ■ ∈ { 0 , 1 } Square (1,4), Red Patch x 15 ■ ∈ { 0 , 1 } x_{15\redbox} \in \B x 15 ■ ∈ { 0 , 1 } Square (1,5), Red Patch x 16 ■ ∈ { 0 , 1 } x_{16\redbox} \in \B x 16 ■ ∈ { 0 , 1 } Square (1,6), Red Patch x 21 ■ ∈ { 0 , 1 } x_{21\redbox} \in \B x 21 ■ ∈ { 0 , 1 } Square (2,1), Red Patch x 22 ■ ∈ { 0 , 1 } x_{22\redbox} \in \B x 22 ■ ∈ { 0 , 1 } Square (2,2), Red Patch x 23 ■ ∈ { 0 , 1 } x_{23\redbox} \in \B x 23 ■ ∈ { 0 , 1 } Square (2,3), Red Patch x 24 ■ ∈ { 0 , 1 } x_{24\redbox} \in \B x 24 ■ ∈ { 0 , 1 } Square (2,4), Red Patch x 25 ■ ∈ { 0 , 1 } x_{25\redbox} \in \B x 25 ■ ∈ { 0 , 1 } Square (2,5), Red Patch x 26 ■ ∈ { 0 , 1 } x_{26\redbox} \in \B x 26 ■ ∈ { 0 , 1 } Square (2,6), Red Patch x 31 ■ ∈ { 0 , 1 } x_{31\redbox} \in \B x 31 ■ ∈ { 0 , 1 } Square (3,1), Red Patch x 32 ■ ∈ { 0 , 1 } x_{32\redbox} \in \B x 32 ■ ∈ { 0 , 1 } Square (3,2), Red Patch x 33 ■ ∈ { 0 , 1 } x_{33\redbox} \in \B x 33 ■ ∈ { 0 , 1 } Square (3,3), Red Patch x 34 ■ ∈ { 0 , 1 } x_{34\redbox} \in \B x 34 ■ ∈ { 0 , 1 } Square (3,4), Red Patch x 35 ■ ∈ { 0 , 1 } x_{35\redbox} \in \B x 35 ■ ∈ { 0 , 1 } Square (3,5), Red Patch x 36 ■ ∈ { 0 , 1 } x_{36\redbox} \in \B x 36 ■ ∈ { 0 , 1 } Square (3,6), Red Patch x 41 ■ ∈ { 0 , 1 } x_{41\redbox} \in \B x 41 ■ ∈ { 0 , 1 } Square (4,1), Red Patch x 42 ■ ∈ { 0 , 1 } x_{42\redbox} \in \B x 42 ■ ∈ { 0 , 1 } Square (4,2), Red Patch x 43 ■ ∈ { 0 , 1 } x_{43\redbox} \in \B x 43 ■ ∈ { 0 , 1 } Square (4,3), Red Patch x 44 ■ ∈ { 0 , 1 } x_{44\redbox} \in \B x 44 ■ ∈ { 0 , 1 } Square (4,4), Red Patch x 45 ■ ∈ { 0 , 1 } x_{45\redbox} \in \B x 45 ■ ∈ { 0 , 1 } Square (4,5), Red Patch x 46 ■ ∈ { 0 , 1 } x_{46\redbox} \in \B x 46 ■ ∈ { 0 , 1 } Square (4,6), Red Patch x 51 ■ ∈ { 0 , 1 } x_{51\redbox} \in \B x 51 ■ ∈ { 0 , 1 } Square (5,1), Red Patch x 52 ■ ∈ { 0 , 1 } x_{52\redbox} \in \B x 52 ■ ∈ { 0 , 1 } Square (5,2), Red Patch x 53 ■ ∈ { 0 , 1 } x_{53\redbox} \in \B x 53 ■ ∈ { 0 , 1 } Square (5,3), Red Patch x 54 ■ ∈ { 0 , 1 } x_{54\redbox} \in \B x 54 ■ ∈ { 0 , 1 } Square (5,4), Red Patch x 55 ■ ∈ { 0 , 1 } x_{55\redbox} \in \B x 55 ■ ∈ { 0 , 1 } Square (5,5), Red Patch x 56 ■ ∈ { 0 , 1 } x_{56\redbox} \in \B x 56 ■ ∈ { 0 , 1 } Square (5,6), Red Patch x 61 ■ ∈ { 0 , 1 } x_{61\redbox} \in \B x 61 ■ ∈ { 0 , 1 } Square (6,1), Red Patch x 62 ■ ∈ { 0 , 1 } x_{62\redbox} \in \B x 62 ■ ∈ { 0 , 1 } Square (6,2), Red Patch x 63 ■ ∈ { 0 , 1 } x_{63\redbox} \in \B x 63 ■ ∈ { 0 , 1 } Square (6,3), Red Patch x 64 ■ ∈ { 0 , 1 } x_{64\redbox} \in \B x 64 ■ ∈ { 0 , 1 } Square (6,4), Red Patch x 65 ■ ∈ { 0 , 1 } x_{65\redbox} \in \B x 65 ■ ∈ { 0 , 1 } Square (6,5), Red Patch x 66 ■ ∈ { 0 , 1 } x_{66\redbox} \in \B x 66 ■ ∈ { 0 , 1 } Square (6,6), Red Patch x 11 ■ ∈ { 0 , 1 } x_{11\bluebox} \in \B x 11 ■ ∈ { 0 , 1 } Square (1,1), Blue Patch x 12 ■ ∈ { 0 , 1 } x_{12\bluebox} \in \B x 12 ■ ∈ { 0 , 1 } Square (1,2), Blue Patch x 13 ■ ∈ { 0 , 1 } x_{13\bluebox} \in \B x 13 ■ ∈ { 0 , 1 } Square (1,3), Blue Patch x 14 ■ ∈ { 0 , 1 } x_{14\bluebox} \in \B x 14 ■ ∈ { 0 , 1 } Square (1,4), Blue Patch x 15 ■ ∈ { 0 , 1 } x_{15\bluebox} \in \B x 15 ■ ∈ { 0 , 1 } Square (1,5), Blue Patch x 16 ■ ∈ { 0 , 1 } x_{16\bluebox} \in \B x 16 ■ ∈ { 0 , 1 } Square (1,6), Blue Patch x 21 ■ ∈ { 0 , 1 } x_{21\bluebox} \in \B x 21 ■ ∈ { 0 , 1 } Square (2,1), Blue Patch x 22 ■ ∈ { 0 , 1 } x_{22\bluebox} \in \B x 22 ■ ∈ { 0 , 1 } Square (2,2), Blue Patch x 23 ■ ∈ { 0 , 1 } x_{23\bluebox} \in \B x 23 ■ ∈ { 0 , 1 } Square (2,3), Blue Patch x 24 ■ ∈ { 0 , 1 } x_{24\bluebox} \in \B x 24 ■ ∈ { 0 , 1 } Square (2,4), Blue Patch x 25 ■ ∈ { 0 , 1 } x_{25\bluebox} \in \B x 25 ■ ∈ { 0 , 1 } Square (2,5), Blue Patch x 26 ■ ∈ { 0 , 1 } x_{26\bluebox} \in \B x 26 ■ ∈ { 0 , 1 } Square (2,6), Blue Patch x 31 ■ ∈ { 0 , 1 } x_{31\bluebox} \in \B x 31 ■ ∈ { 0 , 1 } Square (3,1), Blue Patch x 32 ■ ∈ { 0 , 1 } x_{32\bluebox} \in \B x 32 ■ ∈ { 0 , 1 } Square (3,2), Blue Patch x 33 ■ ∈ { 0 , 1 } x_{33\bluebox} \in \B x 33 ■ ∈ { 0 , 1 } Square (3,3), Blue Patch x 34 ■ ∈ { 0 , 1 } x_{34\bluebox} \in \B x 34 ■ ∈ { 0 , 1 } Square (3,4), Blue Patch x 35 ■ ∈ { 0 , 1 } x_{35\bluebox} \in \B x 35 ■ ∈ { 0 , 1 } Square (3,5), Blue Patch x 36 ■ ∈ { 0 , 1 } x_{36\bluebox} \in \B x 36 ■ ∈ { 0 , 1 } Square (3,6), Blue Patch x 41 ■ ∈ { 0 , 1 } x_{41\bluebox} \in \B x 41 ■ ∈ { 0 , 1 } Square (4,1), Blue Patch x 42 ■ ∈ { 0 , 1 } x_{42\bluebox} \in \B x 42 ■ ∈ { 0 , 1 } Square (4,2), Blue Patch x 43 ■ ∈ { 0 , 1 } x_{43\bluebox} \in \B x 43 ■ ∈ { 0 , 1 } Square (4,3), Blue Patch x 44 ■ ∈ { 0 , 1 } x_{44\bluebox} \in \B x 44 ■ ∈ { 0 , 1 } Square (4,4), Blue Patch x 45 ■ ∈ { 0 , 1 } x_{45\bluebox} \in \B x 45 ■ ∈ { 0 , 1 } Square (4,5), Blue Patch x 46 ■ ∈ { 0 , 1 } x_{46\bluebox} \in \B x 46 ■ ∈ { 0 , 1 } Square (4,6), Blue Patch x 51 ■ ∈ { 0 , 1 } x_{51\bluebox} \in \B x 51 ■ ∈ { 0 , 1 } Square (5,1), Blue Patch x 52 ■ ∈ { 0 , 1 } x_{52\bluebox} \in \B x 52 ■ ∈ { 0 , 1 } Square (5,2), Blue Patch x 53 ■ ∈ { 0 , 1 } x_{53\bluebox} \in \B x 53 ■ ∈ { 0 , 1 } Square (5,3), Blue Patch x 54 ■ ∈ { 0 , 1 } x_{54\bluebox} \in \B x 54 ■ ∈ { 0 , 1 } Square (5,4), Blue Patch x 55 ■ ∈ { 0 , 1 } x_{55\bluebox} \in \B x 55 ■ ∈ { 0 , 1 } Square (5,5), Blue Patch x 56 ■ ∈ { 0 , 1 } x_{56\bluebox} \in \B x 56 ■ ∈ { 0 , 1 } Square (5,6), Blue Patch x 61 ■ ∈ { 0 , 1 } x_{61\bluebox} \in \B x 61 ■ ∈ { 0 , 1 } Square (6,1), Blue Patch x 62 ■ ∈ { 0 , 1 } x_{62\bluebox} \in \B x 62 ■ ∈ { 0 , 1 } Square (6,2), Blue Patch x 63 ■ ∈ { 0 , 1 } x_{63\bluebox} \in \B x 63 ■ ∈ { 0 , 1 } Square (6,3), Blue Patch x 64 ■ ∈ { 0 , 1 } x_{64\bluebox} \in \B x 64 ■ ∈ { 0 , 1 } Square (6,4), Blue Patch x 65 ■ ∈ { 0 , 1 } x_{65\bluebox} \in \B x 65 ■ ∈ { 0 , 1 } Square (6,5), Blue Patch x 66 ■ ∈ { 0 , 1 } x_{66\bluebox} \in \B x 66 ■ ∈ { 0 , 1 } Square (6,6), Blue Patch x 11 ■ ∈ { 0 , 1 } x_{11\magentabox} \in \B x 11 ■ ∈ { 0 , 1 } Square (1,1), Magenta Patch x 12 ■ ∈ { 0 , 1 } x_{12\magentabox} \in \B x 12 ■ ∈ { 0 , 1 } Square (1,2), Magenta Patch x 13 ■ ∈ { 0 , 1 } x_{13\magentabox} \in \B x 13 ■ ∈ { 0 , 1 } Square (1,3), Magenta Patch x 14 ■ ∈ { 0 , 1 } x_{14\magentabox} \in \B x 14 ■ ∈ { 0 , 1 } Square (1,4), Magenta Patch x 15 ■ ∈ { 0 , 1 } x_{15\magentabox} \in \B x 15 ■ ∈ { 0 , 1 } Square (1,5), Magenta Patch x 16 ■ ∈ { 0 , 1 } x_{16\magentabox} \in \B x 16 ■ ∈ { 0 , 1 } Square (1,6), Magenta Patch x 21 ■ ∈ { 0 , 1 } x_{21\magentabox} \in \B x 21 ■ ∈ { 0 , 1 } Square (2,1), Magenta Patch x 22 ■ ∈ { 0 , 1 } x_{22\magentabox} \in \B x 22 ■ ∈ { 0 , 1 } Square (2,2), Magenta Patch x 23 ■ ∈ { 0 , 1 } x_{23\magentabox} \in \B x 23 ■ ∈ { 0 , 1 } Square (2,3), Magenta Patch x 24 ■ ∈ { 0 , 1 } x_{24\magentabox} \in \B x 24 ■ ∈ { 0 , 1 } Square (2,4), Magenta Patch x 25 ■ ∈ { 0 , 1 } x_{25\magentabox} \in \B x 25 ■ ∈ { 0 , 1 } Square (2,5), Magenta Patch x 26 ■ ∈ { 0 , 1 } x_{26\magentabox} \in \B x 26 ■ ∈ { 0 , 1 } Square (2,6), Magenta Patch x 31 ■ ∈ { 0 , 1 } x_{31\magentabox} \in \B x 31 ■ ∈ { 0 , 1 } Square (3,1), Magenta Patch x 32 ■ ∈ { 0 , 1 } x_{32\magentabox} \in \B x 32 ■ ∈ { 0 , 1 } Square (3,2), Magenta Patch x 33 ■ ∈ { 0 , 1 } x_{33\magentabox} \in \B x 33 ■ ∈ { 0 , 1 } Square (3,3), Magenta Patch x 34 ■ ∈ { 0 , 1 } x_{34\magentabox} \in \B x 34 ■ ∈ { 0 , 1 } Square (3,4), Magenta Patch x 35 ■ ∈ { 0 , 1 } x_{35\magentabox} \in \B x 35 ■ ∈ { 0 , 1 } Square (3,5), Magenta Patch x 36 ■ ∈ { 0 , 1 } x_{36\magentabox} \in \B x 36 ■ ∈ { 0 , 1 } Square (3,6), Magenta Patch x 41 ■ ∈ { 0 , 1 } x_{41\magentabox} \in \B x 41 ■ ∈ { 0 , 1 } Square (4,1), Magenta Patch x 42 ■ ∈ { 0 , 1 } x_{42\magentabox} \in \B x 42 ■ ∈ { 0 , 1 } Square (4,2), Magenta Patch x 43 ■ ∈ { 0 , 1 } x_{43\magentabox} \in \B x 43 ■ ∈ { 0 , 1 } Square (4,3), Magenta Patch x 44 ■ ∈ { 0 , 1 } x_{44\magentabox} \in \B x 44 ■ ∈ { 0 , 1 } Square (4,4), Magenta Patch x 45 ■ ∈ { 0 , 1 } x_{45\magentabox} \in \B x 45 ■ ∈ { 0 , 1 } Square (4,5), Magenta Patch x 46 ■ ∈ { 0 , 1 } x_{46\magentabox} \in \B x 46 ■ ∈ { 0 , 1 } Square (4,6), Magenta Patch x 51 ■ ∈ { 0 , 1 } x_{51\magentabox} \in \B x 51 ■ ∈ { 0 , 1 } Square (5,1), Magenta Patch x 52 ■ ∈ { 0 , 1 } x_{52\magentabox} \in \B x 52 ■ ∈ { 0 , 1 } Square (5,2), Magenta Patch x 53 ■ ∈ { 0 , 1 } x_{53\magentabox} \in \B x 53 ■ ∈ { 0 , 1 } Square (5,3), Magenta Patch x 54 ■ ∈ { 0 , 1 } x_{54\magentabox} \in \B x 54 ■ ∈ { 0 , 1 } Square (5,4), Magenta Patch x 55 ■ ∈ { 0 , 1 } x_{55\magentabox} \in \B x 55 ■ ∈ { 0 , 1 } Square (5,5), Magenta Patch x 56 ■ ∈ { 0 , 1 } x_{56\magentabox} \in \B x 56 ■ ∈ { 0 , 1 } Square (5,6), Magenta Patch x 61 ■ ∈ { 0 , 1 } x_{61\magentabox} \in \B x 61 ■ ∈ { 0 , 1 } Square (6,1), Magenta Patch x 62 ■ ∈ { 0 , 1 } x_{62\magentabox} \in \B x 62 ■ ∈ { 0 , 1 } Square (6,2), Magenta Patch x 63 ■ ∈ { 0 , 1 } x_{63\magentabox} \in \B x 63 ■ ∈ { 0 , 1 } Square (6,3), Magenta Patch x 64 ■ ∈ { 0 , 1 } x_{64\magentabox} \in \B x 64 ■ ∈ { 0 , 1 } Square (6,4), Magenta Patch x 65 ■ ∈ { 0 , 1 } x_{65\magentabox} \in \B x 65 ■ ∈ { 0 , 1 } Square (6,5), Magenta Patch x 66 ■ ∈ { 0 , 1 } x_{66\magentabox} \in \B x 66 ■ ∈ { 0 , 1 } Square (6,6), Magenta Patch x 11 ■ ∈ { 0 , 1 } x_{11\brickbox} \in \B x 11 ■ ∈ { 0 , 1 } Square (1,1), Brick Patch x 12 ■ ∈ { 0 , 1 } x_{12\brickbox} \in \B x 12 ■ ∈ { 0 , 1 } Square (1,2), Brick Patch x 13 ■ ∈ { 0 , 1 } x_{13\brickbox} \in \B x 13 ■ ∈ { 0 , 1 } Square (1,3), Brick Patch x 14 ■ ∈ { 0 , 1 } x_{14\brickbox} \in \B x 14 ■ ∈ { 0 , 1 } Square (1,4), Brick Patch x 15 ■ ∈ { 0 , 1 } x_{15\brickbox} \in \B x 15 ■ ∈ { 0 , 1 } Square (1,5), Brick Patch x 16 ■ ∈ { 0 , 1 } x_{16\brickbox} \in \B x 16 ■ ∈ { 0 , 1 } Square (1,6), Brick Patch x 21 ■ ∈ { 0 , 1 } x_{21\brickbox} \in \B x 21 ■ ∈ { 0 , 1 } Square (2,1), Brick Patch x 22 ■ ∈ { 0 , 1 } x_{22\brickbox} \in \B x 22 ■ ∈ { 0 , 1 } Square (2,2), Brick Patch x 23 ■ ∈ { 0 , 1 } x_{23\brickbox} \in \B x 23 ■ ∈ { 0 , 1 } Square (2,3), Brick Patch x 24 ■ ∈ { 0 , 1 } x_{24\brickbox} \in \B x 24 ■ ∈ { 0 , 1 } Square (2,4), Brick Patch x 25 ■ ∈ { 0 , 1 } x_{25\brickbox} \in \B x 25 ■ ∈ { 0 , 1 } Square (2,5), Brick Patch x 26 ■ ∈ { 0 , 1 } x_{26\brickbox} \in \B x 26 ■ ∈ { 0 , 1 } Square (2,6), Brick Patch x 31 ■ ∈ { 0 , 1 } x_{31\brickbox} \in \B x 31 ■ ∈ { 0 , 1 } Square (3,1), Brick Patch x 32 ■ ∈ { 0 , 1 } x_{32\brickbox} \in \B x 32 ■ ∈ { 0 , 1 } Square (3,2), Brick Patch x 33 ■ ∈ { 0 , 1 } x_{33\brickbox} \in \B x 33 ■ ∈ { 0 , 1 } Square (3,3), Brick Patch x 34 ■ ∈ { 0 , 1 } x_{34\brickbox} \in \B x 34 ■ ∈ { 0 , 1 } Square (3,4), Brick Patch x 35 ■ ∈ { 0 , 1 } x_{35\brickbox} \in \B x 35 ■ ∈ { 0 , 1 } Square (3,5), Brick Patch x 36 ■ ∈ { 0 , 1 } x_{36\brickbox} \in \B x 36 ■ ∈ { 0 , 1 } Square (3,6), Brick Patch x 41 ■ ∈ { 0 , 1 } x_{41\brickbox} \in \B x 41 ■ ∈ { 0 , 1 } Square (4,1), Brick Patch x 42 ■ ∈ { 0 , 1 } x_{42\brickbox} \in \B x 42 ■ ∈ { 0 , 1 } Square (4,2), Brick Patch x 43 ■ ∈ { 0 , 1 } x_{43\brickbox} \in \B x 43 ■ ∈ { 0 , 1 } Square (4,3), Brick Patch x 44 ■ ∈ { 0 , 1 } x_{44\brickbox} \in \B x 44 ■ ∈ { 0 , 1 } Square (4,4), Brick Patch x 45 ■ ∈ { 0 , 1 } x_{45\brickbox} \in \B x 45 ■ ∈ { 0 , 1 } Square (4,5), Brick Patch x 46 ■ ∈ { 0 , 1 } x_{46\brickbox} \in \B x 46 ■ ∈ { 0 , 1 } Square (4,6), Brick Patch x 51 ■ ∈ { 0 , 1 } x_{51\brickbox} \in \B x 51 ■ ∈ { 0 , 1 } Square (5,1), Brick Patch x 52 ■ ∈ { 0 , 1 } x_{52\brickbox} \in \B x 52 ■ ∈ { 0 , 1 } Square (5,2), Brick Patch x 53 ■ ∈ { 0 , 1 } x_{53\brickbox} \in \B x 53 ■ ∈ { 0 , 1 } Square (5,3), Brick Patch x 54 ■ ∈ { 0 , 1 } x_{54\brickbox} \in \B x 54 ■ ∈ { 0 , 1 } Square (5,4), Brick Patch x 55 ■ ∈ { 0 , 1 } x_{55\brickbox} \in \B x 55 ■ ∈ { 0 , 1 } Square (5,5), Brick Patch x 56 ■ ∈ { 0 , 1 } x_{56\brickbox} \in \B x 56 ■ ∈ { 0 , 1 } Square (5,6), Brick Patch x 61 ■ ∈ { 0 , 1 } x_{61\brickbox} \in \B x 61 ■ ∈ { 0 , 1 } Square (6,1), Brick Patch x 62 ■ ∈ { 0 , 1 } x_{62\brickbox} \in \B x 62 ■ ∈ { 0 , 1 } Square (6,2), Brick Patch x 63 ■ ∈ { 0 , 1 } x_{63\brickbox} \in \B x 63 ■ ∈ { 0 , 1 } Square (6,3), Brick Patch x 64 ■ ∈ { 0 , 1 } x_{64\brickbox} \in \B x 64 ■ ∈ { 0 , 1 } Square (6,4), Brick Patch x 65 ■ ∈ { 0 , 1 } x_{65\brickbox} \in \B x 65 ■ ∈ { 0 , 1 } Square (6,5), Brick Patch x 66 ■ ∈ { 0 , 1 } x_{66\brickbox} \in \B x 66 ■ ∈ { 0 , 1 } Square (6,6), Brick Patch x 11 ■ ∈ { 0 , 1 } x_{11\brownbox} \in \B x 11 ■ ∈ { 0 , 1 } Square (1,1), Brown Patch x 12 ■ ∈ { 0 , 1 } x_{12\brownbox} \in \B x 12 ■ ∈ { 0 , 1 } Square (1,2), Brown Patch x 13 ■ ∈ { 0 , 1 } x_{13\brownbox} \in \B x 13 ■ ∈ { 0 , 1 } Square (1,3), Brown Patch x 14 ■ ∈ { 0 , 1 } x_{14\brownbox} \in \B x 14 ■ ∈ { 0 , 1 } Square (1,4), Brown Patch x 15 ■ ∈ { 0 , 1 } x_{15\brownbox} \in \B x 15 ■ ∈ { 0 , 1 } Square (1,5), Brown Patch x 16 ■ ∈ { 0 , 1 } x_{16\brownbox} \in \B x 16 ■ ∈ { 0 , 1 } Square (1,6), Brown Patch x 21 ■ ∈ { 0 , 1 } x_{21\brownbox} \in \B x 21 ■ ∈ { 0 , 1 } Square (2,1), Brown Patch x 22 ■ ∈ { 0 , 1 } x_{22\brownbox} \in \B x 22 ■ ∈ { 0 , 1 } Square (2,2), Brown Patch x 23 ■ ∈ { 0 , 1 } x_{23\brownbox} \in \B x 23 ■ ∈ { 0 , 1 } Square (2,3), Brown Patch x 24 ■ ∈ { 0 , 1 } x_{24\brownbox} \in \B x 24 ■ ∈ { 0 , 1 } Square (2,4), Brown Patch x 25 ■ ∈ { 0 , 1 } x_{25\brownbox} \in \B x 25 ■ ∈ { 0 , 1 } Square (2,5), Brown Patch x 26 ■ ∈ { 0 , 1 } x_{26\brownbox} \in \B x 26 ■ ∈ { 0 , 1 } Square (2,6), Brown Patch x 31 ■ ∈ { 0 , 1 } x_{31\brownbox} \in \B x 31 ■ ∈ { 0 , 1 } Square (3,1), Brown Patch x 32 ■ ∈ { 0 , 1 } x_{32\brownbox} \in \B x 32 ■ ∈ { 0 , 1 } Square (3,2), Brown Patch x 33 ■ ∈ { 0 , 1 } x_{33\brownbox} \in \B x 33 ■ ∈ { 0 , 1 } Square (3,3), Brown Patch x 34 ■ ∈ { 0 , 1 } x_{34\brownbox} \in \B x 34 ■ ∈ { 0 , 1 } Square (3,4), Brown Patch x 35 ■ ∈ { 0 , 1 } x_{35\brownbox} \in \B x 35 ■ ∈ { 0 , 1 } Square (3,5), Brown Patch x 36 ■ ∈ { 0 , 1 } x_{36\brownbox} \in \B x 36 ■ ∈ { 0 , 1 } Square (3,6), Brown Patch x 41 ■ ∈ { 0 , 1 } x_{41\brownbox} \in \B x 41 ■ ∈ { 0 , 1 } Square (4,1), Brown Patch x 42 ■ ∈ { 0 , 1 } x_{42\brownbox} \in \B x 42 ■ ∈ { 0 , 1 } Square (4,2), Brown Patch x 43 ■ ∈ { 0 , 1 } x_{43\brownbox} \in \B x 43 ■ ∈ { 0 , 1 } Square (4,3), Brown Patch x 44 ■ ∈ { 0 , 1 } x_{44\brownbox} \in \B x 44 ■ ∈ { 0 , 1 } Square (4,4), Brown Patch x 45 ■ ∈ { 0 , 1 } x_{45\brownbox} \in \B x 45 ■ ∈ { 0 , 1 } Square (4,5), Brown Patch x 46 ■ ∈ { 0 , 1 } x_{46\brownbox} \in \B x 46 ■ ∈ { 0 , 1 } Square (4,6), Brown Patch x 51 ■ ∈ { 0 , 1 } x_{51\brownbox} \in \B x 51 ■ ∈ { 0 , 1 } Square (5,1), Brown Patch x 52 ■ ∈ { 0 , 1 } x_{52\brownbox} \in \B x 52 ■ ∈ { 0 , 1 } Square (5,2), Brown Patch x 53 ■ ∈ { 0 , 1 } x_{53\brownbox} \in \B x 53 ■ ∈ { 0 , 1 } Square (5,3), Brown Patch x 54 ■ ∈ { 0 , 1 } x_{54\brownbox} \in \B x 54 ■ ∈ { 0 , 1 } Square (5,4), Brown Patch x 55 ■ ∈ { 0 , 1 } x_{55\brownbox} \in \B x 55 ■ ∈ { 0 , 1 } Square (5,5), Brown Patch x 56 ■ ∈ { 0 , 1 } x_{56\brownbox} \in \B x 56 ■ ∈ { 0 , 1 } Square (5,6), Brown Patch x 61 ■ ∈ { 0 , 1 } x_{61\brownbox} \in \B x 61 ■ ∈ { 0 , 1 } Square (6,1), Brown Patch x 62 ■ ∈ { 0 , 1 } x_{62\brownbox} \in \B x 62 ■ ∈ { 0 , 1 } Square (6,2), Brown Patch x 63 ■ ∈ { 0 , 1 } x_{63\brownbox} \in \B x 63 ■ ∈ { 0 , 1 } Square (6,3), Brown Patch x 64 ■ ∈ { 0 , 1 } x_{64\brownbox} \in \B x 64 ■ ∈ { 0 , 1 } Square (6,4), Brown Patch x 65 ■ ∈ { 0 , 1 } x_{65\brownbox} \in \B x 65 ■ ∈ { 0 , 1 } Square (6,5), Brown Patch x 66 ■ ∈ { 0 , 1 } x_{66\brownbox} \in \B x 66 ■ ∈ { 0 , 1 } Square (6,6), Brown Patch Solving Patches ¶ Let’s import the Patcheslinkedin_games library that was design to solve the Patches game by using LOP modeling with Pyomo.
The Patches class needs two inputs to be instantiated:
grid_dimsThe grid dimensions of the Patches game. seedsA dictionary of patch seeds on the grid, which must follow the bellow structure: {
(row, column) : {
"color": "color name or its hex code",
"area": int | None
"shape": "vertical" | "horizontal" | "square" | "any" | None
}, ...
}from linkedin_games import Patches
seeds = {
(1,2): {"color": "#846A0B", "area": 2},
(1,4): {"color": "#096B78", "area": 6},
(2,6): {"color": "#5A3DB1", "area": 2},
(3,1): {"color": "#0A7541", "area": 6},
(3,3): {"color": "#EF6C00", "area": 2, "shape":"vertical"},
(4,4): {"color": "#E30102", "area": 4, "shape":"square"},
(4,6): {"color": "#097BB1", "area": 2},
(5,1): {"color": "#A01E4E", "area": 2},
(6,3): {"color": "#9B3C1C", "area": 6},
(6,5): {"color": "#503B36", "area": 4},
}
patches = Patches(6, seeds)
The Pacthes class features the model attribute, which implements the PatchesModel object to structure the Linear Optimization logic behind the Patches’ game.
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from typing import Any
import pyomo.environ as pyo
from ..base.shikaku._model import ShikakuModel
from ._patch_shape import PatchShape
class PatchesModel(ShikakuModel):
"""The Linear Optimization model for the Patches game."""
def __init__(self, grid_dims: tuple[int, int], seeds: list[dict[str, Any]]) -> None:
"""
Args:
grid_dims: Grid dimensionas as `(rows, columns)` tuple.
seeds: Patch seeds on the grid as a dictionary of
`(row, column): {"color": str, "area": int, "shape": str}`.
"""
super().__init__(grid_dims, seeds)
# RANGE SETS
K = self.K # Rectangles
# COMPOSITE SETS
V = self.V = pyo.Set( # Vertical rectangles
initialize=[seed["color_code"] for seed in seeds if seed["shape"] == PatchShape.VERTICAL], domain=K
)
H = self.H = pyo.Set( # Horizontal rectangles
initialize=[seed["color_code"] for seed in seeds if seed["shape"] == PatchShape.HORIZONTAL], domain=K
)
Q = self.Q = pyo.Set( # Squared rectangles
initialize=[seed["color_code"] for seed in seeds if seed["shape"] == PatchShape.SQUARE], domain=K
)
# DECISION VARIABLES
h = self.h # Height of rectangle k
w = self.w # Width of rectangle k
# CONSTRAINTS
## Rectangle Seed Constraints
self.vertical_rectangles_constraints = pyo.Constraint(
V, rule=lambda model, k: h[k] >= w[k] + 1
)
self.horizontal_rectangles_constraints = pyo.Constraint(
H, rule=lambda model, k: w[k] >= h[k] + 1
)
self.square_rectangles_constraints = pyo.Constraint(
Q, rule=lambda model, k: h[k] == w[k]
)
Program 1: Creating the model with Pyomo components.
With the model built, the public method solve() calls the restricted method _set_solution() to save the solution to _grid and __patches attributes, which can be accessed by the public solution and patches attributes, respectively.
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A game grid with some colored rectangle seeds that may state some features about the rectanglesProgram 2: Saving the solution on grid and patch attributes after solving the game’s model.
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A game grid with some colored rectangle seeds that may state some features about the rectanglesProgram 3: Implementation of patches attribute.
With the solution obtained, the method show() plots the solved Patches’ grid.
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A game grid with some colored rectangle seeds that may state some features about the rectanglesProgram 4: Implementation of show() function.
So to solve the game and display its results, just call the public methods solve() and show(), at this order.
patches.solve()
patches.show()Running above block, the method show() returns the solved game, which matches the official solution of Patches No. 16, as expected.
Figure 5: Solved instance visualization.
