How to perform it

  1. Scatter the coins. Drop six to ten coins on the table so some land heads and some tails. Glance at them and count the heads. Remember only whether that number is odd or even.
  2. Turn your back. Ask your volunteer to turn over any coin they like, one at a time, saying “flip” out loud each time. They may flip the same coin more than once.
  3. Keep track. Every time you hear “flip”, switch your mental note between odd and even. Start at what you saw: if there were 4 heads you start at “even”, and after one flip you think “odd”, after two “even”, and so on.
  4. Cover one. When they are done, ask them to cover any one coin with their hand.
  5. Turn around and count. Count the heads you can see. Is that number odd or even?
  6. Name the coin. If the visible heads match your mental note (both odd or both even), the hidden coin is tails. If they do not match, the hidden coin is heads.

Why it works: every flip changes the number of heads by exactly one, so it switches between odd and even. If you count the flips, you always know whether the total is odd or even. Then the covered coin is whatever makes the visible count add up.

Tips for clean counting

  • Keep a single word in your head. “Even … odd … even.” Do not try to keep a running number.
  • Ask for a pace. “Nice and steady, so I can’t hear which coin.” The real reason is so you do not miss a flip.
  • If you lose count, do not guess. Ask them to stop, turn around “to check the coins are all still on the table”, note whether the heads are odd or even, and turn your back again for a fresh round.

Making it a routine

Do it twice at most. The second time, have them cover the chosen coin with an upturned cup instead of a hand, and announce your answer before the cup is lifted. Iris writes hers on a card first, which makes the counting look like reading.

Credit where due: A classic parity principle from recreational mathematics. We simulated 20,000 random rounds of flips and covers; the method named the covered coin correctly every time, provided the flips were counted correctly.

Next: The 1089 book test