The 22 Game

A Classic Puzzle by Henry Ernest Dudeney

Lay out sixteen cards as shown.
1 hearts 1 spades 1 diamonds 1 clubs
2 hearts 2 spades 2 diamonds 2 clubs
3 hearts 3 spades 3 diamonds 3 clubs
4 hearts 4 spades 4 diamonds 4 clubs

Two players alternately turn down a card and add it to the common score, and the player who makes the score of 22, or forces his opponent to go beyond that number, wins. For example, A turns down a 4, B turns down a 3 (counting 7), A turns down a 4 (counting 11), B plays a 2 (counting 13), A plays 1 (14), B plays 3 (17), and whatever A does, B scores the winning 22 next play. Again, supposing the play was 3-1, 1-2, 3-3, 1-2, 1-4, scoring 21, the second player would win again, because there is no 1 left and his opponent must go beyond 22.

Which player should always win, and how?


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