A Walk Through Combinatorics 4th Ed.1. 2.

***Disclaimer: This is NOT the solution being looked for by the author/ professor/ whomever. This is a number theoretic solution, just in case you're terrible at combinatorics (like I am). If you want the combinatorial solution, refer to the solutions page in the book. Godspeed.***

IMO, combinatorics exists so people in the continuous math camp (analysis, topology, diff. eq.'s) can't look at people in the non-continuous camp (number theory, algebra, logic) and say "lol your math is ez."

^^^Of course that's a bad joke. Everybody has their strengths and weaknesses. Analysis is certainly no friend of mine. Yet during undergrad, number theory, set theory, and even graduate-level algebra courses barely made me break a sweat. So you'd think I had my home in those types of math... but combinatorics, man, so often for me is like competing in a mental triathlon.

Anyways, sorry for my rant. Here's a number theoretic solution to this little puzzle, in case you're interested.