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HMMT 十一月 2008 · 团队赛 · 第 1 题

HMMT November 2008 — Team Round — Problem 1

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

  1. (a) Decompose 1 into unit fractions.
    (b) Decompose into unit fractions.1
    (c) Decompose into unit fractions.24
    15

英文原题

Explain why 4 is not a juicy number.

解析

英文解析

  1. Explain why 4 is not a juicy number.
    Solution: If 4 were juicy, then we would have 1 = . . . + . The . . . can only possible contain 1
    1 1 1 1 1 1 1 1 14
    and , but it is clear that + , + , and + + are all not equal to 1.
    2 3 2 4 3 4 2 3 4