Enumeration Solitaire is a one-player card game with a two-sentence rule set and a genuinely nontrivial answer. You shuffle a deck, deal cards face up, and count "ace, two, three, ..., king" over and over as you go. If the rank you speak ever matches the rank of the card you just dealt, you lose. Get through all 52 cards without a match and you win.

It is a four-copy generalization of the classical probleme des rencontres (the derangement problem), and the solution is one inclusion-exclusion argument compressed into one generating function.

Our working notes: Enumeration Solitaire.

The Problem

This one …