A Proof of Willcocks's Conjecture

TL;DR

This paper proves Willcocks's Conjecture, demonstrating that under certain coprimality conditions, a Hamiltonian tour exists for a specific chess piece on a square board, resolving an open problem from 1976.

Contribution

The paper provides a formal proof of Willcocks's Conjecture, establishing the existence of Hamiltonian tours for (p, q)-leapers under the specified conditions.

Findings

Proof of Willcocks's Conjecture completed

Existence of Hamiltonian tours for (p, q)-leapers proven

Conjecture resolved after 47 years

Abstract

We give a proof of Willcocks's Conjecture, stating that if $p - q$ and $p + q$ are relatively prime, then there exists a Hamiltonian tour of a $(p, q)$-leaper on a square chessboard of side $2(p + q)$. The conjecture was formulated by T. H. Willcocks in 1976 and has been an open problem since.