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I've got it... He picks ten coins at random from the pile of 100, it doesn't matter which ones. Then he flips those coins over. These are his two piles.
If he chose 10 black coins, then he would have flipped them and had 10 white in both piles.
If he chose 9 black and 1 white, then he would have flipped them and had 9 white in the new pile and guess what? there are nine white in the larger pile too.
Repeat for all numbers of coins, still works.
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