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HMMT 二月 2013 · 冲刺赛 · 第 3 题

HMMT February 2013 — 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 rightmost non-zero digit of the expansion of (20)(13!).
解析
  1. [ 4 ] Find the rightmost non-zero digit of the expansion of (20)(13!). Answer: 6 We can rewrite this as (10 ∗ 2)(13 ∗ 12 ∗ 11 ∗ 10 ∗ 9 ∗ 8 ∗ 7 ∗ 6 ∗ 5 ∗ 4 ∗ 3 ∗ 2 ∗ 1) = 3 (10 )(2 ∗ 13 ∗ 12 ∗ 11 ∗ 9 ∗ 8 ∗ 7 ∗ 6 ∗ 4 ∗ 3); multiplying together the units digits for the terms not equal to 10 reveals that the rightmost non-zero digit is 6.