HMMT 二月 2023 · 冲刺赛 · 第 8 题
HMMT February 2023 — Guts Round — Problem 8
题目详情
- [11] Suppose a , b , and c are distinct positive integers such that a b c is an integer. Compute the least possible value of a + b + c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HMMT February 2023, February 18, 2023 — GUTS ROUND Organization Team Team ID#
解析
- [11] Suppose a , b , and c are distinct positive integers such that a b c is an integer. Compute the least possible value of a + b + c . Proposed by: Sean Li Answer: 7 Solution: First, check that no permutation of (1 , 2 , 3) works, so the sum must be more than 6. Then √ √ √ since ( a, b, c ) = (2 , 4 , 1) has 2 4 1 = 2, the answer must be 2 + 4 + 1 = 7.