Link to revised PSet
Last time I mentioned that the last two questions of HW4 seemed too hard (or at least too tedious), so I've revised those to be a little simpler. We're still asking you to think about how to count up the mismatched sets that Boofernaut can wear, but the number of colors is reduced from 5 to 4, which ought to make this easier to think through.
The last question is now one about rearranging a set of 3 colors into distinct orders, and I decided to actually give the answer but challenge students to fill in the possibilities. In general, we've found this is a decent strategy for making problems easier to attack: The uncertainty of knowing whether or not you're done is a big stumbling block sometimes.
Somewhat unrelated to the homework, but I just finished Siobhain Roberts' book "Genius at Play" about John Conway, who is an incredible mathematician who you can find lurking around the biographies of other incredible mathematicians and in lots of material about recreational mathematics. His own biography is fantastic and includes lots of great descriptions of games, puzzles, and pure mathematics.