Math & Logic · Ages 18+
Riddle #213
A pile of 21 stones sits between two players. They take turns removing 1, 2, or 3 stones, and whoever takes the last stone wins. Would you rather move first or second, and what is the strategy?
You solved this one before
Open-ended riddle: think it through, then reveal the answer.
Answer: Move first: take 1 stone, then always take 4 minus whatever your opponent just took.
Taking 1 leaves 20, a multiple of 4. From then on each full round removes exactly 4 stones, so your opponent always faces a multiple of 4 and you take the last stone. Any pile that is a multiple of 4 loses for whoever has to move.