Math game (removing stones) problem...?

imrandom

2008-07-30 11:04 pm

Alice and Bob play the following game; There are n > 1 stones on the table. They alternate turns where on each turn, the number of stones the player can remove must be a positive divisor of the number of stones on the table. (For example, if there are 18 stones on the table, the player whose turn it is, can remove either 1, 2, 3, 6, 9 or 18 stones)

The player who removes the last stone loses!

If n = 2007, who has the winning strategy ?

更新1:

You can pick the person who's going first...as long as you state who..

回答 (1)

[匿名]

2008-07-31 2:13 am

✔ 最佳答案

If n is even, then the person who's going first has the winning strategy. The winning strategy is always to remove 1 (or other odd number if possible). If n = 2007 then the second player has the winning strategy.

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