HMMT 十一月 2015 · 冲刺赛 · 第 10 题
HMMT November 2015 — Guts Round — Problem 10
题目详情
英文原题
- [ 8 ] Call a string of letters S an almost palindrome if S and the reverse of S differ in exactly two places.
Find the number of ways to order the letters in HM M T T HEM ET EAM to get an almost palindrome.
解析
英文解析
- [ 8 ] Call a string of letters S an almost palindrome if S and the reverse of S differ in exactly two places.
Find the number of ways to order the letters in HM M T T HEM ET EAM to get an almost palindrome.
Proposed by: Yang Liu
Answer: 2160
Note that T, E, A are used an odd number of times. Therefore, one must go in the middle spot and
6!
the other pair must match up. There are are 3 · 2( ) = 2160 ways to fill in the first six spots with the
2!
letters T, H, E, M, M and a pair of different letters. The factor of 3 accounts for which letter goes inthe middle.