尼姆
Mathematical strategy - take the last object
- 2 人
- 3–10 分钟
- 难度中等
大厅
暂无开放房间
开一个房间，正在浏览的任何人都能加入。
- 从一行中移除任意数量的棋子
- 必须至少移除一个
- 拿走最后一个的玩家失败
- 数学策略决定胜负
常见问题
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).