Linear Programming, Kakuro Puzzles, Gurobi, Puzzle Game, Discrete Optimization.
variable, x_{i,j,k} · k is simply the value k when k is placed in the cell (i,j). By summing x_{i,j,k} · k over every k and every cell in the horizontal sum, we get the sum of the values placed in the empty cells of the horizontal run. We want that sum to be equal to the horizontal clue, which is