Friday, November 18, 2011

Question First vs Answer First

Among the interests represented on my blog, puzzles are the oldest.  Writing puzzles used to be a hobby of mine back in high school, when I'd write and submit puzzles to a website.  Naturally, the website was full of expert puzzle solvers, so that explains why I am unable to write a puzzle of reasonable difficulty.

In high school, I had a half-baked philosophy of puzzle-writing.  There are essentially two ways to write a puzzle: Question First, or Answer First.

In the Answer First method, first you think up a clever idea.  And then you try to design a puzzle such that the clever idea is the answer.  For example, a folk remedy for hiccups is to scare someone.  So there's a classic riddle based on this idea:
A man walks into a bar and asks for a glass of water.  The bartender pulls out a gun, and the man thanks her.  What happened?
I've also written Answer First puzzles of my own.  "Fast Clock, Slow Clock" is an unambiguous example, as is "Guess the Meaning".  You can usually recognize Answer First puzzles by their clever "Aha!" solutions.  All riddles are Answer First puzzles.

In the Question First method, first you think of an interesting problem.  And then you check to see if there's an interesting solution to it.  For example, a recent puzzle, "Tower of Hanoi Variant" is clearly a Question First puzzle.  I was inspired by a problem posed in the game of Freecell; I only tried to find a solution after the fact.

The Answer First method requires quite a bit of creative insight to use, but the Question First method has its own difficulties.  When you find an interesting question, there is no guarantee that there is a solution, or that the solution is interesting.  And a lot of times, you don't want to just think up one interesting question, you want to think up a whole set of interesting questions.  And then you have to look at all of those questions, and see which one has the most interesting answer.

For example, in "Ten Rows of Three", I asked solvers to arrange nine dots into ten rows of three.  But I could just as easily ask solvers to arrange X dots into Y rows of Z.  What values of X, Y, and Z lead to the most interesting puzzle?

So not only do I need to find a solution without any hints, or even a guarantee that a solution exists, as a puzzle-writer I also have to solve a much larger set of puzzles than the puzzle-solver.  This is my secret to being good at puzzle-solving.  Write lots of puzzles and then you will become very good at solving them.

But I am not sure that the Question First vs Answer First dichotomy applies to all puzzles (that's why I say the philosophy is half-baked).  For example, where does Fillomino fit in?  Designing one of these puzzles involves filling more and more clues in, while trying to see what deductions you can make from those clues.  But often, the clues we fill in are decided by something that the designer wants in the solution.  Depending on the puzzle-designer, it could be more Question First or more Answer First.

My inner skeptic wanted to write a comparison between the Question/Answer First methods of puzzle-writing and the experimental/theoretical methods of science.  But my inner skeptic's inner skeptic said that this is ridiculous.