Linear Programming, Kakuro Puzzles, Gurobi, Puzzle Game, Discrete Optimization.
x_{i,j,k} = 1 signals that we are placing the number k in the cell (i,j). These are the only variables used in our model, thus making it a BILP. We can illustrate our binary variables in the following manner. Due to the board, i and j are constrained by the height and width of the board