熄灯游戏的几个缩影

arXiv - MATH - History and Overview Pub Date : 2024-03-15 DOI:arxiv-2403.17967

Adriano Verdério, Izabele D'Agostin, Mari Sano, Patrícia Massae Kitani

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引用次数: 0

摘要

熄灯游戏背后的理论已由多位作者提出。本作品的目的是利用线性代数提出与该游戏相关的一些结果。我们为这个游戏在 $m$ 乘 $n$ 网格的情况下的可解性建立了一个标准，这个标准取决于矩阵的可逆性，我们提出了发生这种情况的条件，从 $m$ 和 $n$ 可以很容易地验证。此外，我们还明确确定了特定情况下的行列式值。

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Algumas luminescências sobre o jogo Lights Out

The theory behind the Lights Out game has been developed by several authors. The aim of this work is to present some results related to this game using Linear Algebra. We establish a criterion for the solubility of this game in the case of an $m$ by $n$ grid, which depends on the invertibility of a matrix, and we present the conditions for this to occur, easily verifiable from $m$ and $n$. Furthermore, we explicitly determine the value of the determinant for a particular case.

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arXiv - MATH - History and Overview

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