# The 22 Game

 Apart from the exhaustion of cards, the winning series is 7, 12, 17, 22. If you can score 17 and leave at least one 5-pair of both kinds (4-1, 3-2), you must win. If you can score 12 and leave two 5-pairs of both kinds, you must win. If you can score 7 and leave three 5-pairs of both kinds, you must win. Thus, if the first player plays a 3 or 4, you play a 4 or 3, as the case may be, and score 7. Nothing can now prevent the second player from scoring 12, 17, and 22. The lead of 2 can also always be defeated if you reply with a 3 or a 2. Thus 2-3, 2-3, 2-3, 2-3 (20), and, as there is no remaining 2, second player wins. Again, 2-3, 1-3, 3-2, 3-2 (19), and second player wins. Again, 2-3, 3-4 (12), or 2-3, 4-3 (12), also win for second player. The intricacies of the defence 2-2 I leave to the reader. The best second play of a first player is always 1. The first player can always win if he plays 1, and in no other way. Here are specimen games: 1-1, 4-1, 4-1, 4 (16) wins. 1-3, 1-2, 4-1, 4-1, 4 (21) wins. 1-4, 2 (7) wins. 1-2, 4 (7) wins.