HMMT 十一月 2024 · 团队赛 · 第 4 题
HMMT November 2024 — Team Round — Problem 4
题目详情
- [35] Albert writes down all of the multiples of 9 between 9 and 999 , inclusive. Compute the sum of the digits he wrote. ◦
解析
- [35] Albert writes down all of the multiples of 9 between 9 and 999, inclusive. Compute the sum of the digits he wrote. Proposed by: Jackson Dryg Answer: 1512 Solution: If x is a multiple of 9, so is 999 − x , and their digits always sum to 27. The 112 multiples from 0 to 999 form 56 such pairs, so the sum of their digits is 56 · 27 = 1512 . ◦