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HMMT 二月 2014 · 冲刺赛 · 第 35 题

HMMT February 2014 — Guts Round — Problem 35

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 25 ] How many times does the letter “e” occur in all problem statements in this year’s HMMT Februarycompetition?
    If C is the actual answer to this question and A is your answer, then your score on this problem isd max { 25(1 | log ( C/A ) | ) , 0 } e . 2
解析

英文解析

  1. [ 25 ] How many times does the letter “e” occur in all problem statements in this year’s HMMT Februarycompetition?
    If C is the actual answer to this question and A is your answer, then your score on this problem isd max { 25(1 − | log ( C/A ) | ) , 0 }e .
    Answer: 1661 It is possible to arrive at a good estimate using Fermi estimation. See http:2 //en.wikipedia.org/wiki/Fermi_problem for more details.
    For example, there are 76 problems on the HMMT this year. You might guess that the average numberof words in a problem is approximately 40, and the average number of of letters in a word is about 5.
    The frequency of the letter ”e” in the English language is about 10%, resulting in an estimate of
    76 · 40 · 5 · 0 . 1 = 1520 .
    This is remarkably close to the actual answer.