Exploring mod2 n-queens games

TL;DR

This paper introduces a two-player game involving placing queens on an n x n chessboard with move availability based on modulo two attack counts, exploring its rules, variations, and computational complexity.

Contribution

It presents a novel combinatorial game based on mod2 attack counts, analyzing its rules, variations, and complexity, which has not been studied before.

Findings

Game rules and variations defined and analyzed.

Complexity of the game investigated.

Potential strategic insights discussed.

Abstract

We introduce a two player game on an n x n chessboard where queens are placed by alternating turns on a chessboard square whose availability is determined by the number of queens already on the board which can attack that square modulo two. The game is explored along with some variations and its complexity.