MathDB

M2734

Part of Kvant 2023

Problems(1)

Real numbers on vertices of polygon

Source: Kvant Magazine No. 2 2023 M2734

4/19/2023
Real numbers are placed at the vertices of an nn{}-gon. On each side, we write the sum of the numbers on its endpoints. For which nn{} is it possible that the numbers on the sides form a permutation of 1,2,3,…,n1, 2, 3,\ldots , n?
From the folklore
combinatoricsnumber theory