尼姆
Mathematical strategy - take the last object
- 2 人
- 3–10 分鐘
- 難度中等
大廳
目前沒有開放房間
開一間房間，正在瀏覽的任何人都能加入。
- 從一排中取走任意數量的棋子
- 必須至少取走一個棋子
- 取走最後一個棋子的玩家輸
常見問題
Take the last object(s) to win (normal play), or avoid taking the last object (misere variant).
Objects (traditionally matchsticks or stones) are arranged in several piles. Classic setup: rows of 1, 3, 5, and 7 objects (16 total). Many variations exist with different starting configurations.
Win by taking the last object (normal) or forcing your opponent to take it (misere). The winning strategy involves binary XOR calculations of pile sizes.
Players alternate turns. On your turn, remove any number of objects from a single pile (at least one, up to all of them). You can only take from one pile per turn.
Learn the Nim-sum: XOR all pile sizes in binary. If Nim-sum is 0 before your move, you're in a losing position (with perfect opponent play). Always aim to leave a Nim-sum of 0 after your move. With two equal piles, mirror your opponent's moves in the other pile.
Nim was comprehensively analyzed by Charles Bouton in 1901, who proved the winning strategy. The name may come from German 'nimm' (take) or archaic English 'nim' (steal).