5.K.3. CAYLEY'S MOUSETRAP This is a solitaire (= patience) game developed by Cayley, based on Treize. Take a deck of cards, numbered 1, 2, ..., n, and shuffle them. Count through them. If a card does not match its count, put it on bottom and continue. If it matches, set it aside and start counting again from 1. One wins if all cards are set aside. In this case, pick up the deck and start a new game.
T. W. O. Richards, proposer; Richard I. Hess, solver. Prob. 1828. CM 19 (1993) 78 & 20 (1994) 77-78. Asks whether there is any arrangement which allows three or more consecutive wins. No theoretical solution. Searching finds one solution for n = 6 and n = 8 and 8 solutions for n = 9.
