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HMMT 二月 2008 · GEN2 赛 · 第 10 题

HMMT February 2008 — GEN2 Round — Problem 10

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 6 ] Determine the number of 8-tuples of nonnegative integers ( a , a , a , a , b , b , b , b ) satisfying 0 ≤ 1 2 3 4 1 2 3 4 a ≤ k , for each k = 1 , 2 , 3 , 4, and a + a + a + a + 2 b + 3 b + 4 b + 5 b = 19. k 1 2 3 4 1 2 3 4 1
解析
  1. [ 6 ] Determine the number of 8-tuples of nonnegative integers ( a , a , a , a , b , b , b , b ) satisfying 0 ≤ 1 2 3 4 1 2 3 4 a ≤ k , for each k = 1 , 2 , 3 , 4, and a + a + a + a + 2 b + 3 b + 4 b + 5 b = 19. k 1 2 3 4 1 2 3 4 Answer: 1540 Same as Combinatorics Test problem 10. 2