返回题库

HMMT 二月 2017 · 冲刺赛 · 第 5 题

HMMT February 2017 — Guts Round — Problem 5

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 6 ] Find the number of ordered triples of positive integers ( a, b, c ) such that 6 a + 10 b + 15 c = 3000 .
解析
  1. [ 6 ] Find the number of ordered triples of positive integers ( a, b, c ) such that 6 a + 10 b + 15 c = 3000 . Proposed by: Yang Liu Answer: 4851 Note that 6 a must be a multiple of 5, so a must be a multiple of 5. Similarly, b must be a multiple of 3, and c must be a multiple of 2. ( ) 99 Set a = 5 A, b = 3 B, c = 2 C. Then the equation reduces to A + B + C = 100. This has = 4851 2 solutions.