Presentation Title

Applying Group Theory to Peg Solitaire

Presentation Type

Oral Presentation

School

School of Sciences and Social Sciences

Discipline

Mathematics

Mentor

Karen Stanish

Abstract

In this presentation, we will investigate the application of a branch of higher mathematics called group theory to peg solitaire. To play peg solitaire, a peg “jumps” over an adjacent peg. The jumped peg is then removed from the board. The goal is to remove as many pegs from the board as possible, ideally all but one. We will use group theory to discover which holes are the sole possibilities for the last peg to be left at the end of the game. We will also explore algorithms for playing peg solitaire that guarantee only a single peg will remain. By studying the applications of group theory to seemingly simple games, we can gain a better appreciation of the beauty and uses of abstract mathematics.

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Applying Group Theory to Peg Solitaire

In this presentation, we will investigate the application of a branch of higher mathematics called group theory to peg solitaire. To play peg solitaire, a peg “jumps” over an adjacent peg. The jumped peg is then removed from the board. The goal is to remove as many pegs from the board as possible, ideally all but one. We will use group theory to discover which holes are the sole possibilities for the last peg to be left at the end of the game. We will also explore algorithms for playing peg solitaire that guarantee only a single peg will remain. By studying the applications of group theory to seemingly simple games, we can gain a better appreciation of the beauty and uses of abstract mathematics.