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Group 1 to 20 into 10 groups
A={(1,20) (2,19) (3,18) (4,17) (5,16) (6,15) (7,14) (8,13) (9,12) (10,11)}
According to Pigeonhole Principle﹐since the pigeons does not greater than pigeonholes, it is possible to win this game

2006-10-20 00:24:03 補充：
for example, if the number he choose are 1,2,3,4,5,6,7,8,9,10he wins

It is surely possible. The 20 disks can be seperated into 10 pairs and only 10 pairs add up to 21, or more clearly, 1 and 20, 2 and 19, 3 and 18... 10 and 11.
If one disk is turned over from each of the 10 different pairs, no two disks should add up to 21.

If chosen by random, probability is low.
Probability of winning by random choosing
= (2^10) / (20C10)
= 1024 / 184756
= 256 / 46189