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Sum of numbers on adjacent vertices and midpoint is the same

Source: Baltic Way 1995

October 8, 2011
combinatorics proposedcombinatorics

Problem Statement

A polygon with 2n+12n+1 vertices is given. Show that it is possible to assign numbers 1,2,…,4n+21,2,\ldots ,4n+2 to the vertices and midpoints of the sides of the polygon so that for each side the sum of the three numbers assigned to it is the same.
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