圆桌放硬币：先手必胜
N 硬币 1 桌
题目详情
2 players take turns placing coins on a large perfectly round table. Coins can not overlap and all the coin surface must be in contact with the table. The first player who can't place a coin loses. Is it better to play first and is there a winning strategy?
解析
先手有必胜策略。
先手第一步把硬币放在圆桌的正中心。之后每当后手在某处放下一枚硬币，先手就在以圆心为中心对称的位置放下一枚硬币。
由于圆桌中心对称，后手每一次合法落子都会对应一个同样合法的对称位置供先手落子，因此后手先无路可走，先手必胜。