# 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.

## April Challenge 1

### Selecting Sums of Sevens

In the mythical land of Sevenia, the lottery is played with a huge collection of ping pong balls. Each ball is one of seven different colors and contains a number printed on it which is definitely **not** a multiple of seven (the secrets of the lottery are steeped in secrecy; you don't know which numbers are included or how often).

Each week one lucky contestant gets to fish out a bucket of balls. If among those randomly selected balls there is some subset which are all the same color and whose numbers sum to a multiple of seven, the contestant wins seven bags of gold. Of course the seven members of the *Senate of Seven* want to ensure that nobody is guaranteed to win just by picking enough balls.

**The Challenge**: What is the largest number of balls a contestant could draw without being guaranteed a win?

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

Deadline: **Friday, April 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 | October Challenge 1 | January Challenge | February Challenge 1 | February Challenge 2 | March Challenge 1 | March 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