It's a problem from BadCamp Puzzles: http://www-scf.usc.edu/~mearnest/puzzles_by_genre.php
Here is the question: I have 40 dice, all of which are 20-sided. Half are red, half are blue. I roll all of these dice. Show that it will be possible to select a nonzero number of dice such that the red total equals the blue total.
I can't figure it out using combinations. My original idea is to list all possible sums any number red dice can get. But I find it too complicated. Mainly I can't find a good solution to connect the number of dice 20 to the side of dice 20.
Any advice or solution will appreciated. Thanks a lot!