"Minesweeper" and spectrum of discrete Laplacians

TL;DR

This paper explores the mathematical connection between the game Minesweeper and the spectral properties of discrete Laplacian operators, leading to new insights into solution uniqueness and game design.

Contribution

It establishes a link between Minesweeper configurations and spectral properties of discrete Laplacians, proposing a new game variant based on these principles.

Findings

Certain open cell configurations guarantee unique solutions

Spectral properties of discrete Laplacians are key to solution uniqueness

A new Minesweeper-inspired game can be played without a computer

Abstract

The paper is devoted to a problem inspired by the "Minesweeper" computer game. It is shown that certain configurations of open cells guarantee the existence and the uniqueness of solution. Mathematically the problem is reduced to some spectral properties of discrete differential operators. It is shown how the uniqueness can be used to create a new game which preserves the spirit of "Minesweeper" but does not require a computer.