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HMMT 十一月 2012 · 团队赛 · 第 4 题

HMMT November 2012 — Team Round — Problem 4

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 3 ] Let π be a permutation of the numbers from 2 through 2012. Find the largest possible value of log π (2) · log π (3) · · · log π (2012). 2 3 2012
解析
  1. [ 3 ] Let π be a permutation of the numbers from 2 through 2012. Find the largest possible value of log π (2) · log π (3) · · · log π (2012). 2 3 2012 Team Round Answer: 1 Note that 2012 2012 ∏ ∏ log π ( i ) log π ( i ) = i log i i =2 i =2 ∏ 2012 log π ( i ) i =2 = ∏ 2012 log i i =2 = 1 , where the last equality holds since π is a permutation of the numbers 2 through 2012.