HMMT 二月 2000 · ADV 赛 · 第 1 题
HMMT February 2000 — ADV Round — Problem 1
题目详情
- 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 b e rotated to get the other. p p 6 6 1+ i 3 1 i 3
解析
- Assume w e ha v e 4 olors - 1, 2, 3, and 4. Fix the b ottom as olor 1. On the remaining sides y ou an ha v e olors 2, 3, 4 (in that order), or 2, 4, 3, whi h are not rotationally iden ti al. So, there are 2 w a ys to olor it. p 6 2 1 2 3 2 2