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HMMT 二月 2009 · COMB 赛 · 第 1 题

HMMT February 2009 — COMB Round — Problem 1

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 3 ] How many ways can the integers from − 7 to 7 inclusive be arranged in a sequence such that theabsolute value of the numbers in the sequence does not decrease?
解析

英文解析

  1. [ 3 ] How many ways can the integers from − 7 to 7 be arranged in a sequence such that the absolutevalue of the numbers in the sequence is nondecreasing?
    Answer: 128
    Solution: Each of the pairs a , − a must occur in increasing order of a for a = 1 , . . . , 7, but a caneither occur before or after − a , for a total of 2 = 128 possible sequences.7