# 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

### Arboreal ants avoiding alliteration

A colony of ants live on the surface of a dodecahedron (a regular convex polyhedron consisting of 12 regular pentagons connected at 20 vertices). They decide they would like to plant ant-trees on each of the 20 vertices. However, because these ants hate monotony, they insist that a different tree must be planted at each vertex surrounding a given face. Obviously they will need at least five different varieties of trees. Will they need more?

**The Challenge:** What is the fewest different varieties of tree the ants will need to plant one tree on each vertex so that no face is incident to two trees of the same variety?

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

Deadline: **Friday, October 16.**

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

### 2015-2016

September Challenge 1 | September Challenge 2

### 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 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