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HMMT 十一月 2020 · 冲刺赛 · 第 2 题

HMMT November 2020 — Guts Round — Problem 2

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [5] Let a be a positive integer such that 2 a has units digit 4. What is the sum of the possible units digits of 3 a ?
解析
  1. [5] Let a be a positive integer such that 2 a has units digit 4. What is the sum of the possible units digits of 3 a ? Proposed by: Daniel Zhu Answer: 7 Solution: If 2 a has last digit 4, then the last digit of a is either 2 or 7. In the former case, 3 a has last digit 6, and in the latter case, 3 a has last digit 1. This gives a final answer of 6 + 1 = 7.