圆桌放硬币：先手必胜
N 硬币 1 桌
题目详情
量化面试题：圆桌放硬币：先手必胜。
英文原题
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。
英文解析
The table is round and the winning strategy in this game is based on the central symmetry of the table. The first player A places his coin at the exact center of the table. Every time B places a coin A can respond by placing his coin in the symmetric position. With this strategy B is forced to discover new areas and A is guaranteed to place a coin. Therefore B will eventually run out of space and A is certain to win.