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 Would you like to play a game? (Posted on 2004-05-10)
Bologna Sandwich was worried about an upcoming test in Discrete Mathematics and was finding it hard to get to sleep. Bologna awoke early in the morning, aroused by devilish laughter, only to see an impish looking homunculus sitting at the bottom of the bed next to a seemingly infinite pile of chips. Hello, Bologna, it said, would you like to play a little game? This pile contains 43546758443209876 chips and the bottom chip represents your immortal soul. The rules are quite simple. The first player removes some chips, but not all of them. After that we take turns removing some chips.

The only rule now is that a player cannot remove more than the previous player removed in his last turn. The winner is the player who takes the last chip. If I win I get to keep your soul and if you win, you get an A in the test. Would you like to go first or second? This seemed a reasonable bet to Bologna.

Can you give Bologna a strategy for playing no matter how many chips there are? (What if there were just one more chip in the initial pile?)

What if the rule were that one is allowed to take up to twice the number of chips the previous player took?

 No Solution Yet Submitted by SilverKnight Rating: 4.3333 (3 votes)

 Subject Author Date answer for the first part naiem 2004-08-04 01:53:10 Solution. Henry 2004-07-30 16:21:45 re(2): Doubling case Solved Charlie 2004-05-11 09:18:34 re: Doubling case Solved Jer 2004-05-10 22:13:28 re: Doubling case Solved Jer 2004-05-10 22:13:26 re: Is there any way...Yes Tristan 2004-05-10 18:08:03 Doubling case started. Jer 2004-05-10 14:47:50 re: Is there any way... Jer 2004-05-10 14:31:28 A question of size... Iain 2004-05-10 14:30:10 re: Is there any way... Iain 2004-05-10 14:28:43 Is there any way... Charlie 2004-05-10 12:55:51 Solution Iain 2004-05-10 12:46:25 Thoughts Iain 2004-05-10 12:25:34

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