圆桌放硬币
N Coins, 1 Table
题目详情
量化面试题：圆桌放硬币。
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
先手把第一枚硬币放在圆桌中心。之后对后手每一步的落子，先手在关于圆心中心对称的位置落子。
由对称性可知先手永远有合法回应，后手先无路可走，因此
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 is forced to discover new areas and is guaranteed to place a coin. Therefore B will eventually run out of space and A is certain to win.