HMMT 十一月 2015 · 冲刺赛 · 第 10 题

HMMT November 2015 — Guts Round — Problem 10

[ 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

[ 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 in the middle.