# 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.

## October Challenge 1

### Coloring the Plane

Suppose you 2-color the plane - that is, color every point in the plane in one of two colors (red or blue). As you can see from the picture proof below, it is not too difficult to prove that there must be two points exactly 1 inch apart that are colored identically (either both red or both blue, in this case).

What if you 3-color the plane?

**The Challenge**: Prove that no matter how the points of a plane are 3-colored, there will exist two points, exactly 1 inch apart, colored identically.

Submit solutions to Ross 2239G or by email to oscar.levin@unco.edu.

Deadline: **Friday, October 17**

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

### 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