On the number of Knight's tours

Author: Ernesto Mordecki.

Posted: 27/12/2001. Status: Submitted. Prepublicaciones de Matemática de la Universidad de la República, 2001/57.

Abstract: Consider the classical problem of the Knight's tour: find an initial square in an 8 x 8 chess board and a sequence of 63 movements for a knight such that the knight visits every square exactly once. We prove that the number of (open) tours is divisble by 8, and give the upper bound 1.305 x 10³⁵ for this quantity.

Download: ps file (198 Kb).

Return to Mordecki's Articles