HMMT 二月 2017 · 冲刺赛 · 第 3 题

英文解析

3. [ 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 valuesof x .
   Therefore, the final answer is 9 + 2(9 + 9 + 5) = 55 .