I am astounded by the thought that people have put into this challenge. Thanks so much, everybody. I've learned a lot already, and every entry has had a new spin on the problem so I'm really looking forward to what people will come up with over the weekend.

In case anyone was wondering, the Tragic puzzle is just a trivial reduction of a real problem that comes up in a popular variant of the card game Magic: The Gathering. There's a particular variant called "5-Color Magic" (aka "Prismatic") in which every deck comprises at least 250 cards and must contain at least 20 cards of each of the five Magic colors subject to the same rules described in the PFC. The variant is popular enough that when the folks at Magic made Magic Online they wanted to add a 5-Color Magic play option and ran into the problem of automatically verifying that a given deck was legal. One of the programmers wrote an article that vaguely described the problem; that sparked my imagination and I've kept the problem tucked away ever since. From what he said (it's at the end of the column), I'm sure that any of the PFC entries so far would be an improvement over what they've got in place. Y'all rule!