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.

September Challenge 2

Self-Similar Divisions

Any triangle can be divided into smaller triangles, but only sometimes are those smaller triangles all congruent to each other and also similar to the original triangle. Three such divisions are shown below, illustrating that it is possible to find triangles which can be divided into 2, 3 or 4 similar triangles. Are there others? Is there a triangle which can be divided into more than 4 similar triangles?

The Challenge: Find as many different triangles with this property, giving the division for each. The winner this month will be the person who finds the most triangles, or in case of a tie, gives the best proof that no more such triangles exist.

challenge art

Submit solutions to Ross 2239G or by email to oscar.levin@unco.edu.
Deadline: Tuesday, September 30

 

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

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