请教一道数学题

答案不难推理出来是b，但是需要写出严谨的过程，请牛人们帮忙看看应该怎么写，谢谢!
A playing field is filled with 2001 Trolls, 2002 Griffins, and 2003 Dragons. Whenever two animals of different species shake hands, they both instantly disappear and are replaced by an animal of the third species. This game continues for some time, until there is only one species of animal left in the field. Which of the following is a possible end position of such a game?


a) Exactly 5 Trolls remain. b) Exactly 25 Griffins remain. c) Exactly 9 Trolls remain. d) Exactly 4 Dragons remain. e) Exactly 6 Dragons remain.

观察奇偶性可以发现，每一步变换都使TGD奇偶性同时变化。比如初始状态是T=odd,G=even,D=odd，第一步不管哪两种动物握手，最后都是T=E,G=O,D=E，因为每种动物数量变化都是+/-1。而第二步之后一定是T=O,G=E,D=O。 又因为初始状态是T=O,G=E,D=O，所以TG或者GD无法同时为零，不存在只剩下D或者T的情况。所以只有一种动物的时候，一定是奇数个的G。

答案不难推理出来是b，但是需要写出严谨的过程，请牛人们帮忙看看应该怎么写，谢谢!
A playing field is filled with 2001 Trolls, 2002 Griffins, and 2003 Dragons. Whenever two animals of different species shake hands, they both instantly disappear and are replaced by an animal of the third species. This game continues for some time, until there is only one species of animal left in the field. Which of the following is a possible end position of such a game?


a) Exactly 5 Trolls remain. b) Exactly 25 Griffins remain. c) Exactly 9 Trolls remain. d) Exactly 4 Dragons remain. e) Exactly 6 Dragons remain.
tutu1234 发表于 2021-10-19 00:05

對喔 龍有幾隻手?

观察奇偶性可以发现，每一步变换都使TGD奇偶性同时变化。比如初始状态是T=odd,G=even,D=odd，第一步不管哪两种动物握手，最后都是T=E,G=O,D=E，因为每种动物数量变化都是+/-1。而第二步之后一定是T=O,G=E,D=O。 又因为初始状态是T=O,G=E,D=O，所以TG或者GD无法同时为零，不存在只剩下D或者T的情况。所以只有一种动物的时候，一定是奇数个的G。
lauraoyzj 发表于 2021-10-19 01:04

谢谢，简单明了，太厉害了，我绕了一大圈才得出答案

對喔 龍有幾隻手?
phlin 发表于 2021-10-19 04:49

这个你要看是哪国的龙了。。