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HMMT 二月 2007 · GEN1 赛 · 第 1 题

HMMT February 2007 — GEN1 Round — Problem 1

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 2 ] Michael has 16 white socks, 3 blue socks, and 6 red socks in a drawer. Ever the lazy college student,
    he has overslept and is late for his favorite team’s season-opener. Because he is now in such a rush toget from Harvard to Foxborough, he randomly takes socks from the drawer (one at a time) until hehas a pair of the same color. What is the largest number of socks he could possibly withdraw in thisfashion?
解析

英文解析

  1. [ 2 ] Michael has 16 white socks, 3 blue socks, and 6 red socks in a drawer. Ever the lazy college student,
    he has overslept and is late for his favorite team’s season-opener. Because he is now in such a rush toget from Harvard to Foxborough, he randomly takes socks from the drawer (one at a time) until hehas a pair of the same color. What is the largest number of socks he could possibly withdraw in thisfashion?
    Answer: 4 . It is possible for him to begin with three socks of different colors, but an instance of the
    Pigeon Hole Principle is that among any four objects of three types some two are the same type.