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 monthly.  

November Challenge

Tiny Triangles in Huge Hexagons

You can divide a regular hexagon into equilateral triangles by drawing lines parallel to the sides of the hexagon.  For example, a hexagon with side length 2 can be divided into equilateral triangles with side length 1 as shown below.  This creates a certain number of triangles, a certain number of vertices of those triangles (each shared by two, three or six triangles) and a certain number of unit line segments (each shared by one or two triangles).

The Challenge: How many triangles, vertices and line segments will there be when a regular hexagon of side length 100 is divided into triangles with side length 1?  What is the relationship between these numbers?

challenge art

Submit solutions to Ross 2239G or by email to oscar.levin@unco.edu.
Deadline: Wednesday, November 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

2016-2017

September Challenge | October Challenge

2015-2016

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 2 | April Challenge

2014-2015

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

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 2 | April Challenge 1 | April Challenge 2

2012 - 2013

September Challenge | October ChallengeNovember Challenge | January Challenge | February Challenge  | March Challenge  | April Challenge

2011 - 2012

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