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HMMT 十一月 2021 · 冲刺赛 · 第 13 题

HMMT November 2021 — Guts Round — Problem 13

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. [9] Find the number of ways in which the nine numbers 1 , 12 , 123 , 1234 , . . . , 123456789 can be arranged in a row so that adjacent numbers are relatively prime.
解析
  1. [9] Find the number of ways in which the nine numbers 1 , 12 , 123 , 1234 , . . . , 123456789 can be arranged in a row so that adjacent numbers are relatively prime. Proposed by: Sean Li Answer: 0 Solution: The six numbers 12, 123, 12345, 123456, 12345678, and 123456789 are divisible by 3, so they cannot be adjacent. However, arranging six numbers in a row with no two adjacent requires at least 11 numbers, which is impossible.