HMMT 二月 2013 · 冲刺赛 · 第 3 题
HMMT February 2013 — Guts Round — Problem 3
题目详情
英文原题
- [ 4 ] Find the rightmost non-zero digit of the expansion of (20)(13!).
解析
英文解析
- [ 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) =
(10 )(2 ∗ 13 ∗ 12 ∗ 11 ∗ 9 ∗ 8 ∗ 7 ∗ 6 ∗ 4 ∗ 3); multiplying together the units digits for the terms not equal 3
to 10 reveals that the rightmost non-zero digit is 6.