HMMT 二月 2000 · ADV 赛 · 第 1 题
HMMT February 2000 — ADV Round — Problem 1
题目详情
英文原题
- Ho w man y di eren t w a ys are there to pain t the sides of a tetrahedron with exa tly
4 olors? Ea h side gets its o wn olor, and t w o olorings are the same if one an be rotated to get the other.
p p
6 6
1+ i 3 1 i 3
解析
英文解析
- Assume we have 4 olors - 1, 2, 3, and 4. Fix the b ottom as olor 1. On the remainingsides y ou an have olors 2, 3, 4 (in that order), or 2, 4, 3, which are not rotationallyiden ti al. So, there are 2 w a ys to olor it.
6 p
2 1 2 3 2 2