一道比较动脑子的数学题

一道比较动脑子的数学题
一个盒子里放了一些球,每个球不是黑色就是白色,在盒子外面也放了一些球,用来做游戏.
我们从盒子里拿出任意2个球,如果它们的颜色一样,就把它们扔了,从盒子外面的球里拿一个黑色的球放进去.如果它们的颜色不一样,那么把白球放回盒子里,把黑球扔了.按照这种玩法,盒子里的球每次会减少一个,直到盒子里只有一个球时,游戏结束.
游戏开始时,盒子里有21个白球和32个黑球,当你用上面的方法玩游戏,你能确认那最后一个剩下来的球的颜色吗?
英文原文
Consider an urn filled with a number of balls,each of which is either black or white.There are also enough balls outside the urn to play the following game:
We take any two balls from the urn.If they both have the same colour,throw them away but put another black ball into the urn.If they have different colours,then return the white one to the urn and throw the black one away.Each execution of the above process reduces the number of balls in the urn by one; when only one ball is left in the urn,the game is over.
Initially,there are 21 white balls and 32 black balls in the urn.Can you determine the colour of the last ball when you play the game?Justify your answer.
把思考的详细过程给我下 我想理解