# “Lights Out” and Variants

• Published in 2017
In the collection
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.

## Other information

journal
The American Mathematical Monthly: Vol 124
volume
124
number
10

### BibTeX entry

@article{LightsOutandVariants,
title = {“Lights Out” and Variants},
author = {Martin Kreh},
url = {https://www.tandfonline.com/doi/abs/10.4169/amer.math.monthly.124.10.937},
urldate = {2019-12-09},
year = 2017,
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.},
comment = {},
journal = {The American Mathematical Monthly: Vol 124},
volume = 124,
number = 10,
collections = {puzzles}
}