Puzzles
The Blind Bartender's Four Glasses
Four glasses sit at the corners of a square turntable, each either right-side up or upside down — but you're blindfolded. Each turn you may touch any two glasses and flip either, both, or neither; then the table spins to a random new position. A bell rings the moment all four glasses match. Can you guarantee the bell eventually rings?
Reveal the answer
Yes. There's a fixed, non-random sequence of at most five moves that's guaranteed to make all four glasses match no matter how the table has spun in between — you never need to see the glasses or track the spins, only follow the sequence. Martin Gardner introduced it as 'the blind bartender's problem' in his Scientific American 'Mathematical Games' column, February 1979.