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HMMT 二月 2017 · 冲刺赛 · 第 3 题

HMMT February 2017 — Guts Round — Problem 3

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [ 4 ] Find the number of pairs of integers ( x, y ) such that x + 2 y < 25 .
解析
  1. [ 4 ] Find the number of pairs of integers ( x, y ) such that x + 2 y < 25 . Proposed by: Allen Liu Answer: 55 We do casework on y . 2 2 If y = 0, we have x < 25, so we get 9 values of x . If y = ± 1, then x < 23, so we still have 9 values 2 2 of x . If y = ± 2, we have x < 17, so we have 9 values of x . If y = ± 3, we have x < 7, we get 5 values of x . Therefore, the final answer is 9 + 2(9 + 9 + 5) = 55 .