Two Player Lights Out

Two Player Lights Out

Presenter(s)

Maximo Gonzalez

Comments

10:45-12:00, Kennedy Union Ballroom

Description

This is a project for MTH 466, Graph Theory and Combinatorics. A graph is a mathematical object that consists of two sets, a set of vertices and a set of edges. An edge joins two vertices and depicts a relationship between those vertices, and these vertices are called neighbors. This game is played on a graph, all of whose vertices can be thought of as lights which can be “off” and “on”. Selecting a vertex changes the state of that vertex and of all its neighbors. At the start of the game, the lights at all the vertices are on. The two players take turns in selecting a vertex of the graph. A player may not select the same vertex that their opponent selected most recently. The winner is the player who turns off the last light. If the lights remain on after 20 turns, then the game is a draw. This poster investigates the fewest required moves for a player to win, whether the order of moves matter, and whether there is an advantage to being the first player.

Publication Date

4-23-2025

Project Designation

Course Project - MTH 466 01

Primary Advisor

Aparna W. Higgins

Primary Advisor's Department

Mathematics

Keywords

Stander Symposium, College of Arts and Sciences

Two Player Lights Out

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