Mousetrap is the name of a game introduced by the English mathematician Arthur Cayley. In the game, cards numbered
1
n
1,2,3,...
1
n+1
In order for at least one card to be removed, the initial permutation of the cards must not be a derangement. However, this is not a sufficient condition for winning, because it does not take into account subsequent removals. The number of ways the cards can be arranged such that the entire game is won, for n = 1, 2, ..., are
1, 1, 2, 6, 15, 84, 330, 1812, 9978, 65503, ... .
For example with four cards, the probability of winning is 0.25, but this reduces as the number of cards increases, and with thirteen cards it is about 0.0046.