# Permutation Groups and Puzzle Tile Configurations of Instant Insanity II

## Degree Name

MS (Master of Science)

## Program

Mathematical Sciences

5-2014

Robert A. Beeler

## Committee Members

Robert Gardner, Debra Knisley, Rick Norwood

## Abstract

The manufacturer claims that there is only one solution to the puzzle Instant Insanity II. However, a recent paper shows that there are two solutions. Our goal is to find ways in which we only have one solution. We examine the permutation groups of the puzzle and use modern algebra to attempt to fix the puzzle. First, we find the permutation group for the case when there is only one empty slot at the top. We then examine the scenario when we add an extra column or an extra row to make the game a 4 × 5 puzzle or a 5 x 4 puzzle, respectively. We consider the possibilities when we delete a color to make the game a 3 × 3 puzzle and when we add a color, making the game a 5 × 5 puzzle. Finally, we determine if solution two is a permutation of solution one.

## Document Type

Thesis - unrestricted