Checkerboard Relay Problem
Relay questions can come in many forms. They typically start with let T = TNYWR (The Number You Will Receive). The idea is you can do a lot of work on solving the problem before you know what T is. Then when you receive T from a teammate, you can finish up your problem and get your answer.
Relays appear on mathleague.org High School competitions and on ARML, www.arml.com, competitions.
This particular question is explained at http://puzzles.nigelcoldwell.co.uk/twentyseven.htm, along with lots of other places. A video explanation is at https://www.youtube.com/watch?v=HUkN-AuYs2I
An extension of the problem is explained on a video at http://mathcounts.org/resources/video-library/mathcounts-minis/mini-21-counting-rectangles-gridsquares-lattice-grid