变色龙同色问题
Chameleon Colors
题目详情
岛上有 13 只红变色龙、15 只绿变色龙、17 只蓝变色龙。
当两只不同颜色的变色龙相遇时，它们都会变成第三种颜色。
问：是否可能经过一系列相遇，使得最终所有变色龙都变成同一种颜色？
There are 13 red chameleons, 15 green chameleons, and 17 blue chameleons on an island. When two chameleons of different colors meet, they both change into the third color. Is it possible for all chameleons to become the same color eventually?
解析
不可能。
用模 3 不变量：每次相遇会让三种颜色数量按特定方式变化，但某个线性组合在模 3 意义下保持不变，因此无法从初始状态到达“全同色”的目标状态（目标态对应不变量值不同）。
Original Explanation
No, it is impossible. A typical solution uses mod 3 arguments or parity arguments. The color counts move in such a way that their remainders (mod 3) cannot all align to produce a single color count of all 45. Hence you can show a contradiction if you assume they eventually all become one color.