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HMMT 十一月 2016 · 冲刺赛 · 第 7 题

HMMT November 2016 — Guts Round — Problem 7

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 7 ] What is the minimum value of the product
    ∏6
    a − ai i +1
    a − ai +2 i +3
    i =1
    given that ( a , a , a , a , a , a ) is a permutation of (1 , 2 , 3 , 4 , 5 , 6)? (note a = a , a = a · · · )
    1 2 3 4 5 6 7 1 8 2
解析

英文解析

  1. [ 7 ] What is the minimum value of the product
    ∏6
    a − ai i +1
    a − ai +2 i +3
    i =1
    given that ( a , a , a , a , a , a ) is a permutation of (1 , 2 , 3 , 4 , 5 , 6)? (note a = a , a = a · · · )
    1 2 3 4 5 6 7 1 8 2
    Proposed by: Kevin Sun
    Answer: 1
    The product always evaluates to 1 .