From reader Derek Christie:
Each player in a game of cribbage has a hand of four cards. A single further card is turned up and serves as the fifth card in every player’s hand. Part of the game involves scoring your hand. You get points for any combination of cards that adds to 15, like 9 4 2; for two or more of any rank, like 3 3; or for any run of three or more, like Ace 2 3. The Jack, Queen, and King each score 10. Show that if a 5 has been turned up, every player must score some points.