HMMT 十一月 2009 · 冲刺赛 · 第 10 题

HMMT November 2009 — Guts Round — Problem 10

[ 8 ] Admiral Ackbar needs to send a 5-character message through hyperspace to the Rebels. Each character is a lowercase letter, and the same letter may appear more than once in a message. When the message is beamed through hyperspace, the characters come out in a random order. Ackbar chooses 1 his message so that the Rebels have at least a chance of getting the same message he sent. How 2 many distinct messages could he send?

解析

[ 8 ] Admiral Ackbar needs to send a 5-character message through hyperspace to the Rebels. Each character is a lowercase letter, and the same letter may appear more than once in a message. When the message is beamed through hyperspace, the characters come out in a random order. Ackbar chooses 1 his message so that the Rebels have at least a chance of getting the same message he sent. How 2 many distinct messages could he send? Answer: 26 If there is more than one distinct letter sent in the message, then there will be at most a 1/5 chance of transmitting the right message. So the message must consist of one letter repeated five times, so there are 26 possible messages.