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.  

September Challenge

Tetris for Bees

When bees play Tetris, they use hexagons instead of squares.  That is, each playing piece is made up of four adjacent hexagons, in some configuration (a hexa-tetromino).  The goal of the game is to completely cover a regular n x n x n hexagonal grid with non-overlapping playing pieces.  For example, the 4x4x4 grid below is partially covered with playing pieces, although this might not be a correct start.  You can use the same shape as many or as few times as you like.

The Challenge: For which n is it possible to completely cover a regular n x n x n hexagonal grid with non-overlapping hexa-tetrominos?  Prove your answer.

challenge art

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

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 - 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