HMMT 二月 2024 · 冲刺赛 · 第 9 题
HMMT February 2024 — Guts Round — Problem 9
题目详情
- [7] Compute the sum of all positive integers n such that n − 3000 is a perfect square.
解析
- Compute the sum of all positive integers n such that n − 3000 is a perfect square. There are 86 teams participating in the Guts rounds. Of these, the distribution of answers to Problem 1 is as follows: • 49 teams submitted 0 , the correct answer. • 17 teams submitted 1872 , the correct answer to Problem 9. • 3 teams submitted 3744 , twice the correct answer to Problem 9. • 2 teams submitted each of 55 and 744 . • 1 team submitted each of the following answers: 20, 548, 1404, 1586, 1772, 1807, 1817, 1882, 2184, 2746, 4680, 7488, and 9360. The distribution of answers to Problem 9 is as follows: • 69 teams submitted 1872 , the correct answer. • 5 teams submitted 3744 , twice the correct answer. • 2 teams submitted 2184 . • 1 team submitted each of the following answers: 55, 205, 548, 1560, 1764, 1772, 1832, 1867, 1893, and 3634.