HMMT 二月 2021 · 冲刺赛 · 第 1 题

HMMT February 2021 — Guts Round — Problem 1

[8] Amelia wrote down a sequence of consecutive positive integers, erased one integer, and scrambled the rest, leaving the sequence below. What integer did she erase? 6 , 12 , 1 , 3 , 11 , 10 , 8 , 15 , 13 , 9 , 7 , 4 , 14 , 5 , 2

解析

[8] Amelia wrote down a sequence of consecutive positive integers, erased one integer, and scrambled the rest, leaving the sequence below. What integer did she erase? 6 , 12 , 1 , 3 , 11 , 10 , 8 , 15 , 13 , 9 , 7 , 4 , 14 , 5 , 2 Proposed by: Andrew Gu Answer: 16 Solution: The sequence of positive integers exactly contains every integer between 1 and 15, inclusive. 16 is the only positive integer that could be added to this sequence such that the resulting sequence could be reordered to make a sequence of consecutive positive integers. Therefore, Amelia must have erased the integer 16.