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HMMT 二月 2001 · 冲刺赛 · 第 12 题

HMMT February 2001 — Guts Round — Problem 12

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ ± 6] How many distinct sets of 8 positive odd integers sum to 20? 3 2
解析
  1. [ ± 6] How many distinct sets of 8 positive odd integers sum to 20? Solution: This is the same as the number of ways 8 nonnegative even integers sum to 12 (we subtract 1 from each integer in the above sum). All 11 possibilities are (leaving out 0s): 12, 10 + 2, 8 + 4, 8 + 2 + 2, 6 + 6, 6 + 4 + 2, 6 + 2 + 2 + 2 + 2, 4 + 4 + 4, 4 + 4 + 2 + 2, 4 + 2 + 2 + 2 + 2, 2 + 2 + 2 + 2 + 2 + 2. 3 2