HMMT 二月 2014 · 冲刺赛 · 第 35 题

HMMT February 2014 — Guts Round — Problem 35

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

解析

[ 25 ] How many times does the letter “e” occur in all problem statements in this year’s HMMT February competition? If C is the actual answer to this question and A is your answer, then your score on this problem is d max { 25(1 − | log ( C/A ) | ) , 0 }e . 2 Answer: 1661 It is possible to arrive at a good estimate using Fermi estimation. See http: //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 number of 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.