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HMMT 二月 2001 · 团队赛 · 第 1 题

HMMT February 2001 — Team Round — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. How many digits are in the base two representation of 10! (factorial)?
解析
  1. How many digits are in the base two representation of 10! (factorial)? 8 4 2 Solution: We write 10! = 2 · 3 · 5 · 7. The number of digits (base 2) of 10! is equal to 4 2 1 2 2 1 [log 10!] = 8 + log (3 · 5 · 7). Since 2 3 < 3 · 5 · 7 < 2 4, the number of digits is 8 + 13 = 2 2 21 .