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Old 2009-10-30, 14:32   #1
Raman
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"Mr. Tuch"
Dec 2007
Chennai, India

3·419 Posts
Default Very nice strategical puzzle

This is an excellent strategical puzzle to tune up your brains.

There is a box containing n holes. Two players put balls into these holes alternatively. (Assume that the box contains holes along a straight line, so that you cover up these holes in sequence.) Let player 1 start up with the game. Each player can put between min and max balls into the box in one turn. The person who puts the last ball will be the winner or loser, that is decided and fixed prior to the game, randomly.

The values of n, min, max are also decided and fixed prior to the game. For simplicity purposes, let us assume that 20 ≤ n ≤ 50 and then that 1 min < max ≤ 10.

If the person who puts the last ball is the winner, then for what values of n, depending upon min and max, will player 1 win the game, and then for what values of n will player 2 do so? Assume that both the players play so cleverly. Thus, what about the case if the person who puts the last ball is the loser? (If there is less than min slots remaining at the end, then the last player can put less than min balls during his last turn. Otherwise, the minimum number of balls that a player can put up within his turn is min only.)

Last fiddled with by Raman on 2009-10-30 at 14:34
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