KGS math club/solution 11 27
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Split the coins into two piles: 64 and 32 coins. Flip every coin in the pile of 64. Now both piles have equal number of heads.
Proof: let n be the number of heads in the original pile of 32 (so n is between 0 and 32). Now the original pile of 64 has 64-n heads. When every coin is flipped, the pile of 64 has 64-(64-n)=n heads as well.
