Hex implies Y

TL;DR

This paper presents a topological proof that the game of Y cannot end in a draw, extending the Hex Theorem to a new game and simplifying existing proofs.

Contribution

It introduces a topological proof for the impossibility of draws in game Y, generalizing the Hex Theorem without board shape restrictions.

Findings

Game Y cannot end in a draw.

A simplified proof of the Hex Theorem is provided.

The proof is purely topological and shape-independent.

Abstract

We give a simple and short proof of the fact that the board game of Y cannot end in a draw. Our proof, based on the analogous result for the game of Hex (the so-called 'Hex Theorem'), is purely topological and does not depend on the shape of the board. We also include a simplified version of Gale's proof of Hex Theorem.