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regular 2n-gon are labelled with the numbers 1,2,...,2n

Source: Switzerland - Swiss TST 2000 p11

February 19, 2020
combinatoricsregular polygon

Problem Statement

The vertices of a regular 2n2n-gon (n≥3n \ge 3) are labelled with the numbers 1,2,...,2n1,2,...,2n so that the sum of the numbers at any two adjacent vertices equals the sum of the numbers at the vertices diametrically opposite to them. Show that this is only possible if nn is odd.
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