Math Challenge Problem

The Math Challenge problem has returned to UNC's School of Mathematical Sciences! This is a problem that everyone is welcomed to try their hand at. New problems twice a month.

February Challenge 2

Polygon Coloring

Consider polygons containing an even number of edges. You are going to color every other edge red, and color all the others blue. As you can see in the example below, there is no reason to think that the red edges and the blue edges will have the same total length. But of course, the polygon above does not circumscribe a circle. That is, there is no circle to which every edge of the polygon is tangent.

The Challenge: Prove that if a polygon with an even number of edges circumscribes a circle, then coloring every other edge red and the others blue will result in the red edges having the same total length as the blue edges.

challenge art

Submit solutions to Ross 2239G or by email to oscar.levin@unco.edu.
Deadline: Friday, February 27

 

Win PRIZES! A winner will be selected from all correct answers received for each challenge problem to receive a fun math prize of his or her choice.


Previous Problems

2014-2015

September Challenge 1 | September Challenge 2 | October Challenge 1 | January Challenge | February Challeng 1

2013-2014

September Challenge 1 | September Challenge 2 | October Challenge 1 | October Challenge 2 | November Challenge 1 | November Challenge 2 | January Challenge | February Challenge 1 | February Challenge 2 | March Challenge 1 | March Challenge 1 | April Challenge 1 | April Challenge 2

2012 - 2013

September Challenge - Solution | October Challenge |November Challenge | January Challenge - Solution | February Challenge - Solution | March Challenge - Solution | April Challenge

2011 - 2012

Problem 1 (Solution) | Problem 2 (Solution) | Problem 3 | January Challenge (Solution) | February Challenge 1 (Solution) | February Challenge 2 | March Challenge | April Challenge

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Contact Information

  • School of Mathematical Sciences, University of Northern Colorado
  • Ross 2239
  • Campus Box 122
  • 501 20th Street
  • Greeley, CO 80639
  • Tel: (970) 351-2820
  • Fax: (970) 351-1225