Solving the Genius Square: Using Math and Computers to Analyze a Polyomino Tiling Game

This paper investigates if the claim of the game Genius Square is true, that all 62,208 boards that its dice can roll are solvable. The gameboard is a 6 by 6 grid and the objective of the game is to tile a board that has 7 blockers, quasi-randomly placed by the dice, with 9 polyominoes consisting of 1, 2, 3, and 4 squares. In order to implement a model of linear systems created by John Burkardt and M.R. Garvie, code was developed using Python and Matlab. With this code, it was shown that all 62,208 boards are solvable. The number of boards, unrestrained by the game dice, which are solvable and unsolvable was also found. Then, after analyzing unsolvable boards to determine patterns that guarantee unsolvability and taking those patterns into account, a new set of dice were developed. These dice, similar to the default set in the game, always produce solvable boards.