2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116329We give an estimate of the number of geometrically distinct open tours $\G$ for a knight on a chessboard. We use a randomization of Warnsdorff rule to implement importance sampling in a backtracking scheme, correcting the observed bias of the original rule, according to the proposed principle that ``most solutions follow Warnsdorff rule most of the time''. After some experiments in order to test this principle, and to calibrate a parameter, interpreted as a distance of a general solution from a Warnsdorff solution, we conjecture that $\G=1.22\times 10^{15}$.8 pages. See also http://www.cmat.edu.uy/~mordecki/articlesProbabilityCombinatoricstext