Nim游戏(The game of Nim)是一个很著名而且有很多版本的游戏.下面这个版本有一个有趣的获胜策略.两名参与者交替从一堆石子中取出若干数目,其个数由参与者自已决定.但是要求参与者每次至少取出一个,至多取出一半,然后另一名参与者继续.拿到最后一个石子的参与者将输掉该游戏.

编写一个程序,让计算机和人较量.在10到100之间生成一个随机数作为初始的石子数目.然后,随机产生0或1,以决定是计算机先玩还是人先玩.然后,再随机产生0或1,以决定计算机采用"聪明"还是"愚蠢"模式.在愚蠢模式中,在轮到计算机时,简单地取走随机数目(介于1到n/2之间)的石子 在聪明模式中,计算机每次取走一定数目的石子,使得剩下的石子数目是2的某次幂减1,例如3,7,15,31,63.这总是可行的,除非当前的石子数正好是2的某次幂减1.在这种情况下,计算机取走随机数目的石子.

你将会发现,当计算机在聪明模式下且是先下手时,它总是不可击败的,除非原始石子数目很偶然的是2的某次幂减1.例如15,31,63.当然,如果人是先手而且知道获胜策略时,也是可以战胜计算机的.

-Nim game (The game of Nim) is a well-known and there are many versions of the game. Here is an interesting version of a winning strategy. Two players alternately remove stones from the pile of a certain number, the number of the participants own decision. but requires participants to take out at least one time, up to remove the half, and then the other participants to continue. get the last stone of the participants will lose the game.

Write a program that allows computers and the throne. 10 to 100 generate a random number as the initial number of pebbles. And then, randomly generated 0 or 1, to determine whether to play or people get the computer to play first. Then, again randomly produce 0 or 1, to determine the computer using "smart" or "stupid" mode. in stupid mode, the turn of the computer, simply pick random number (from 1 to n/2 between) the stones　in smart mode, the computer each time you pick a certain number of stones, making the number of remaining stones is a power of 2