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mark the vertices of a regular n- gon with numbers from 1 to n

Source: 2021 Saudi Arabia Training Lists p28 https://artofproblemsolving.com/community/c2758131_2021_saudi_arabia_training_tests

January 5, 2022
combinatoricsregular polygon

Problem Statement

Find all positive integer n≥3n\ge 3 such that it is possible to mark the vertices of a regular nn- gon with the number from 1 to n so that for any three vertices A,BA, B and CC with AB=ACAB = AC, the number in AA is greater or smaller than both numbers in B,CB, C.
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