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BdMO National Higher Secondary 2019/5

Source: BdMO National Higher Secondary 2019/5

March 4, 2019
combinatorics

Problem Statement

Prove that for all positive integers nn we can find a permutation of {1,2,...,n1,2,...,n} such that the average of two numbers doesn't appear in-between them.For example {1,3,2,41,3,2,4}works,but {1,4,2,31,4,2,3} doesn't because 22 is between 11 and 33.
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