## Honors Program Theses

#### Title

Solving Lights Out on parity graphs

#### Award/Availability

Honors Program Thesis (UNI Access Only)

Doug Shaw

#### Keywords

Lights out (Game); Games--Mathematics;

#### Abstract

Games and puzzles are important to mathematicians because they provide a fun and engaging environment in which to study complex mathematical concepts. One such game is Lights Out, which was released by Tiger Electronics in 1995. This game consists of a 5x5 grid of lights with the state of each light being either on or off. Whenever a light is pressed, the light switches states along with all of the adjacent lights. The goal of the game is to turn all the lights off.

This game has been studied in detail from a wide variety of perspectives. Anderson and Feil [1] used linear algebra to determine the initial states of the game that are solvable. Torrence [7] examined games that can be solved simply by pressing all the lights that were on in the initial configuration. Arangala and MacDonald [2] have studied variations of Lights Out with different configurations of lights. The game has also been studied in terms of σ+-automata [4][6] and domination theory [3][6].

Mini Lights Out is a variation of Lights Out played on a 4x4 grid of lights. In the 2001 article "Easy Solution to Mini Lights Out," Missigman and Weida [5] define the parity of a light and use that definition to present a simple solution to the game. This thesis explores parity graphs, which have similar properties to Mini Lights Out. Multiple classes of parity graphs are presented, followed by an explanation of how certain parity graphs can be solved in the same way that Missigman and Weida solved Mini Lights Out. Finally, the results of the paper are generalized to include several new cases.

2015

#### Department

Department of Mathematics

#### University Honors Designation

A thesis submitted in partial fulfillment of the requirements for the designation University Honors

2015

#### Object Description

1 PDF file (31 pages)

EN

application/pdf

COinS