Noah Jensen

Senior Project Advisor

Stephanie Treneer

Document Type

Project

Publication Date

Spring 2023

Keywords

Genius Square, Polyominoes, Linear Systems of Equations, Symmetries, Groups, Tiling, Board Game, Coding, Counting

Abstract

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.

Department

Mathematics

Subjects - Topical (LCSH)

Puzzles; Polyominoes; Linear systems; Symmetry (Mathematics); Tiling (Mathematics); Board games

Type

Text

Rights

Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.

Language

English

Format

application/pdf

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