返回题库

HMMT 二月 2025 · 冲刺赛 · 第 1 题

HMMT February 2025 — Guts Round — Problem 1

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [5] Call a 9-digit number a cassowary if it uses each of the digits 1 through 9 exactly once. Compute the number of cassowaries that are prime.
解析
  1. [5] Call a 9-digit number a cassowary if it uses each of the digits 1 through 9 exactly once. Compute the number of cassowaries that are prime. Proposed by: Rishabh Das, Jacob Paltrowitz Answer: 0 Solution: Every cassowary is divisible by 3, as the sum of its digits is 1 + 2 + · · · + 9 = 45. Since all such numbers are divisible by 3 and and greater than 3, none of them are prime. So, there are 0 prime cassowaries.