This is actually a series of puzzles (some of which fall no longer into Q2 but the initial ones do) and I haven't picked a particular one because part of the quality of these puzzles lie in the fact that the whole series is built in the same way, which provides a fair starting point for searching. All those puzzles deal with some meta-aspects of text or letters and reach from surprisingly simple to abstrusely complex. Although I haven't solved a single puzzle of this series (yet), I very much like the theme and enjoy reading the solutions, as they are rather inspiring.
This puzzle does it all. It not only gives a wonderful visual aid that's integral to solving the puzzle, but it also provides many, many different elements of puzzles in its cryptic, twisted text. Solving the puzzle was a true team effort, aided by a large amount of people on the forum. Each stanza had a different way to get to its solution, making the puzzle accessible to a huge population of the puzzlers here. The map itself not only was important to the solution of the puzzle but also contained more than one puzzle in and of itself, making it a fantastic visual.
Any puzzle that can provide so many different puzzles of so many different types inside itself while still maintaining the feel of one overarching puzzle, as well as being able to bring the community together to solve the puzzle as a team, I feel is deserving of the highest praise.
Trevor Powell took a math/logic puzzle that I might have skipped over on its own and turned it into a masterpiece of puzzle exposition. I encourage everybody to at least read the puzzle (even though the write-up is long). The puzzle itself was perhaps a standard logic puzzle (I don't really know what qualities make a puzzle "good"), but I hope that this puzzle leads to more people writing creative fluff for future puzzles!
This puzzle has it all! The presentation is hilarious. From having the magician go off to fight dragons, to having the reader kill the assistant, every detail not only entertains, but serves a purpose to make any potential solution unambiguously verifiable. His premise (the existence of a "magic trick") is surprising, and a solution is far from obvious. However, once you see the solution, it is quite satisfying and clever.
I'm not sure if this is a brand-new type of puzzle, but I've never seen any like it before. The premise is a game of hangman that was lost with only one space left to fill. The solver is given a number of letters that conceivably could have filled the space, with clues to what words would thus have been formed. The challenge is to determine the final state of the game, in the form
The question was: _ p p l e
Alex created a number of these fiendishly simple puzzles, and others were inspired to create some as well. The third puzzle by Alex is lean and elegant, and my nomination for best of the quarter.
The premise of this puzzle is a nice challenge the idea of which should be familiar to any budding logician or fan of Godel, Escher, Bach. It's an 'obvious' idea to come up with once you know about the concept of self-referentiality.
My answer to this question is probably, among my 433+ posts on this site, the one that I've put the most effort into creating. It was an incredible slog and took hours out of my life, but actually getting an answer out at the end made it all worthwhile.
This was a question from a user who had a serious -- and good -- question, and the answer was spot-on.
Not all of our best questions are challenge questions, and the primary reason I like this one is because it suggests that we're still not only capable of, but quite good at answering non-challenge questions from users who visit the site.
This has to be my 2nd nomination for this quarter. Simply because it is so lovingly abstract. While the story-line is fun to read, it also sent my brain buzzing just to understand what the actual question is. Let alone trying to solve it.
This is one of those puzzles, which I'd consider "mathematical" without obviously being so. Something which enlarges one's horizon and forces one to leave the comfort-zone of thinking.
Maybe nothing too special for professional mathematicians - but I'm none :c)