Coin-pile Nim
A pile has 21 coins. Players alternate removing 1, 2, or 3 coins; whoever takes the last coin loses. With perfect play, should you go first or second?
Show hints (2)+
- Find the losing positions: counts ≡ 1 (mod 4).
- 21 ≡ 1 (mod 4) - so the mover loses.
Answer
Reveal answer →Final answer
Go second
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