HMMT 十一月 2023 · 冲刺赛 · 第 16 题
HMMT November 2023 — Guts Round — Problem 16
题目详情
- [10] Compute the number of tuples ( a , a , a , a , a , a ) of (not necessarily positive) integers such that 0 1 2 3 4 5 a ≤ i for all 0 ≤ i ≤ 5 and i a + a + · · · + a = 6 . 0 1 5
解析
- [10] Compute the number of tuples ( a , a , a , a , a , a ) of (not necessarily positive) integers such that 0 1 2 3 4 5 a ≤ i for all 0 ≤ i ≤ 5 and i a + a + · · · + a = 6 . 0 1 5 Proposed by: Rishabh Das Answer: 2002 Solution: Let b = i − a , so b ≥ 0. Then i i i 15 − ( b + b + · · · + b ) = 6 = ⇒ b + b + · · · + b = 9 . 0 1 5 0 1 5 14 By stars and bars, the answer is = 2002. 5