Answers 393below the second player (B) puts off defeat as long as possible. In the second
game he prevents A scoring 17 or 30, but has to give him 24 and 37. In the
third game he prevents A scoring II or 24, but has to give him 17,30, and 37.
Notice the important play of the 3 and the 5.A B A B A B4 I (a) (^4) I 4 I
3 I (b) 3 I 3 4
(II) 2 I (11) 2 3 (d) (17) 5
(17) 5 I (c) 5 I 3 4
3 2 (24) 4 3 (e) (30) 5 (j) I
(24) I 2 5 I 3
(30) 4 (37) 4 (37) 2
3 2
(37) I
(a) Or A will score II next move. (b) B could not prevent A scoring II or
17 next move. (c) Again, to prevent A immediately scoring 24. (d) Prevent-
ing A scoring 17, but giving him 24. (e) Preventing A scoring 30, but giving
him the 37. (j) Thus A can always score 24 (as in the last game) or 30 (as
in this), either of which commands the winning 37.
- 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 playa 4 or 3, as the case may be, and score
- 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 first player is a I.
The first player can always win if he plays I, 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.