Given a polygon with n sides, we assign the numbers 0,1,...,n−1 to the vertices, and to each side is assigned the sum of the numbers assigned to its ends. The figure shows an example for n=5. Notice that the numbers assigned to the sides are still in arithmetic progression.
https://cdn.artofproblemsolving.com/attachments/c/0/975969e29a7953dcb3e440884461169557f9a7.png
∙ Make the respective assignment for a 9-sided polygon, and generalize for odd n.
∙ Prove that this is not possible if n is even. combinatoricsArithmetic Progression