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HMMT 二月 2001 · 冲刺赛 · 第 54 题

HMMT February 2001 — Guts Round — Problem 54

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [10] The set of points ( x , x , x , x ) in R such that x ≥ x ≥ x ≥ x is a cone 1 2 3 4 1 2 3 4 (or hypercone, if you insist). Into how many regions is this cone sliced by the hyperplanes x − x = 1 for 1 ≤ i < j ≤ n ? i j 6 9
解析
  1. [10] The set of points ( x , x , x , x ) in R such that x ≥ x ≥ x ≥ x is a cone 1 2 3 4 1 2 3 4 (or hypercone, if you insist). Into how many regions is this cone sliced by the hyperplanes x − x = 1 for 1 ≤ i < j ≤ n ? i j Solution: C (4) = 14 . 6 9