Nonokenken: Solving Puzzles Using Integer Programs

We examine methods of integer programming in order to solve two of our favorite puzzles: nonograms and KenKen. The former is a puzzle in which each cell of a board must be colored either black or white. The clues provided in the puzzle indicate the number and length of black-cell clusters that must appear in each row and column of the board. The latter, KenKen, is a puzzle that requires the solver to fill an n×n grid of cells with integers from 1 to n such that the solution is a Latin square and adheres to mathematical operation constraints within designated blocks of cells. This paper addresses an IP formation for solving nonograms, various methods which generate nonogram puzzles from images, and an IP formulation for solving KenKen puzzles.