Flip two cups at a time, and one will always stay upside down
Three cups sit in a row: one upside down, two right-side up. You may flip any two cups at once, as many times as you like. Can you ever get all three cups right-side up?
Reveal the answer
No — it's mathematically impossible. Each move flips two cups, changing the number of upside-down cups by exactly 2 (or 0). Starting from 1 upside-down cup, that count can only ever land on an odd number, so it can never reach 0. The trick works as a magic act because the 'easy' starting position — two upside down, one up — is solvable in a single move, and audiences rarely notice the difference.
— Standard recreational-mathematics accounts, Three cups problem