Problem

Source: Bundeswettbewerb Mathematik 2017, Round 2 - #1

Tags: combinatorics, combinatorics unsolved, Sequence, bundeswettbewerb



For which integers $n \geq 4$ is the following procedure possible? Remove one number of the integers $1,2,3,\dots,n+1$ and arrange them in a sequence $a_1,a_2,\dots,a_n$ such that of the $n$ numbers \[ |a_1-a_2|,|a_2-a_3|,\dots,|a_{n-1}-a_n|,|a_n-a_1| \]no two are equal.