You're handed a coin that might be rigged. Can you still use it to make a fair choice?
Suppose you have a coin that lands heads with some unknown probability, not necessarily 50/50. Using only that biased coin, how can you produce a perfectly fair 50/50 outcome, guaranteed unaffected by whatever bias the coin actually has?
Reveal the answer
Flip the coin twice. If you get heads-then-tails, call the result "heads"; if you get tails-then-heads, call it "tails"; if both flips match, discard the result and flip twice again. Because the odds of heads-then-tails always exactly equal the odds of tails-then-heads no matter how biased the coin is, this trick devised by John von Neumann guarantees a perfectly fair result.