HMMT 十一月 2018 · GEN 赛 · 第 4 题
HMMT November 2018 — GEN Round — Problem 4
题目详情
- Find the number of eight-digit positive integers that are multiples of 9 and have all distinct digits.
解析
- Find the number of eight-digit positive integers that are multiples of 9 and have all distinct digits. Proposed by: James Lin Answer: 181440 Note that 0 + 1 + · · · + 9 = 45. Consider the two unused digits, which must then add up to 9. If it’s 0 and 9, there are 8 · 7! ways to finish; otherwise, each of the other four pairs give 7 · 7! ways to finish, since 0 cannot be the first digit. This gives a total of 36 · 7! = 181440.