"Lights Out" and Variants. Issue 10 (1st December 2017)

• Record Type: Journal Article
• Authors: Kreh, Martin
• Is Part Of: American Mathematical Monthly. Volume 124:Issue 10(2017)
• Page Start: 937
• Page End: 950
• Publication Date: 2017-12-01
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.4169/amer.math.monthly.124.10.937
• Languages: English
• ISSNs: 0002-9890

Abstract

Abstract: In this article, we investigate the puzzle "Lights Out" as well as some variants of it (in particular, varying board size and number of colors).We discuss the complete solvability of such games, i.e., we are interested in the cases such that all starting boards can be solved. We will model the problem with basic linear algebra and develop a criterion for the unsolvability depending on the board size modulo 30. Further, we will discuss two ways of handling the solvability that will rely on algebraic number theory.