PUMaC 2019 · 团队赛 · 第 4 题
PUMaC 2019 — Team Round — Problem 4
题目详情
- What is the sum of the leading (first) digits of the integers from 1 to 2019 when the integers are written in base 3? Give your answer in base 10. 3 2
解析
- What is the sum of the leading (first) digits of the integers from 1 to 2019 when the integers are written in base 3? Give your answer in base 10. Proposed by: Nathan Bergman Answer: 2945 For integers from 1 to 2186, there are an equal number with leading digit 1 and leading digit 2 (as 2187 is a power of 3). The integers from 2020 to 2186 all have leading digit 2, so the 3 answer is 2186 ∗ − 2 ∗ 167 = 2945. 2 3 2