100 Coins, Blindfolded

The problem
100 coins · 10 heads up · 90 tails upTTTHTTTTTTTTTTHTTTTTTTTTTTTHTTTHTTTTTTTTTTTTTTTTHTTTTTTTHTTTTTTTTTTTTTTHTTTTTTTHTTTTHTTTTTTTHTTTTTTTblindfolded — split into two piles with equal heads

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.

Tempting (but wrong)
"feel the coins? count them?"TTTHTTTTTTTTTTHTTTTTTTTTTTTHTTTHTTTTTTTTTTTTTTTTHTTTTTTTHTTTTTTTTTTTTTTHTTTTTTTHTTTTHTTTTTTTHTTTTTTT🙈no way to identify heads while blindfolded

The instinctive moves:

  • "Feel for heads." Ruled out — coins are identical to the touch.
  • "Guess and check." No way to check while blindfolded.
  • "Pick 50 and 50." No reason this would balance the heads count — you don't know what you picked.
  • "Randomness will work eventually." Maybe, but the problem asks for a guaranteed strategy.

It feels like you can't act without seeing.