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
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 firstname.lastname@example.org.
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.
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