Three piles of coins

by David Radcliffe

A recent post by Jim Wilder reminded me of the following problem which I heard many years ago.

There are three piles of coins. You are allowed to move coins from one pile to another, but only if the number of coins in the destination pile is doubled. For example, if the first pile has 6 coins and the second pile has 4 coins, then you may move 4 coins from the first pile to the second pile — no more or less. Prove that by repeating moves of this sort, it is possible to empty one of the piles.

I will post my solution in a few days, but I would like to know the origin of this problem. Does anyone know?

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