MathDB

Consider a game on an

n \times n

board, where each square starts with exactly one stone. A move consists of choosing

5

consecutive squares in the same row or column of the board and toggling the state of each of those squares (removing the stone from squares with a stone and placing a stone in squares without a stone). For which positive integers

n \geq 5

is it possible to end up with exactly one stone on the board after a finite number of moves?

Problem Statement