100 Coins, Blindfolded
The problem
A friend places 100 coins on a table. Exactly 10 are heads-up; the other 90 are tails-up. They tell you the counts.
Now they blindfold you. The coins all feel identical, so you cannot identify heads from tails by touch. You can pick up coins and flip them. You can move them into piles.
Split the coins into two piles, each containing the same number of heads.