PUMaC 2017 · 数论（B 组） · 第 1 题
PUMaC 2017 — Number Theory (Division B) — Problem 1
题目详情
- Let a be the least positive integer the sum of whose digits is n . Find a + a + a + · · · + a . n 1 2 3 20
解析
- Clearly a = n for 1 ≤ n ≤ 9. We find that for 10 ≤ n ≤ 18, a = 10( n − 9) + 9 = 10 n − 81, n n e.g. a = 29. We also see that a = 199 and a = 299. Summing gets 1074 . 11 19 20 Problem written by Eric Neyman