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Pairwise Distinct Differences

Source: Bundeswettbewerb Mathematik 2017, Round 2 - #1

September 3, 2017
combinatoricscombinatorics unsolvedSequencebundeswettbewerb

Problem Statement

For which integers n≥4n \geq 4 is the following procedure possible? Remove one number of the integers 1,2,3,…,n+11,2,3,\dots,n+1 and arrange them in a sequence a1,a2,…,ana_1,a_2,\dots,a_n such that of the nn numbers ∣a1−a2∣,∣a2−a3∣,…,∣an−1−an∣,∣an−a1∣ |a_1-a_2|,|a_2-a_3|,\dots,|a_{n-1}-a_n|,|a_n-a_1| no two are equal.
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