Wednesday, June 09, 2004

Problem 2: Coins...

Heard around the dinner table....

I am given n piles of coins, with the knowledge that the total number of coins is 1 + 2 + 3... + n. I take one coin from each pile, and make a new pile. If the ith pile has i coins, this operation leaves all piles unchanged. Prove that no matter what starting configuration of coins in piles I start with, I always end up with this stable configuration.

Answer in a week, or thereabouts...
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