返回题库

HMMT 十一月 2009 · 冲刺赛 · 第 10 题

HMMT November 2009 — Guts Round — Problem 10

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

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

英文解析

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