Friday, February 25, 2005

Solvability

Well, one of the major intents of this blog is to discuss the question of what makes a good puzzle. So, let's start there.

In order to consider something a good puzzle, I as a solver look for it to be four things: Solvable, Challenging, Clever, and Fun. These characteristics are inter-related and share some degree of overlap, but I consider them to be four distinct problems for a constructor to overcome. To allow for discussion and comments and not making posts of an ungodly length, I'll write about each of the four separately, spread out over whenever I get around to it.

Solvable: This requirement seems self-evident to anyone who has never constructed a puzzle (and many who have), but I've found that it can actually be the most difficult to achieve well. For one thing, the sort of person who would consider spending the necessary time and energy to create a puzzle is very often also the sort of person who, despite continuing efforts not to be arrogant about it, takes great pleasure in thinking of themself as smarter than other people. And it's much easier to smoulder internally with malicious pride at the knowledge that you know how something works and no one else can figure it out than it is to take joy in watching others prove that they are as smart as you. I think the best phrasing of this problem (as well as an excellent indicator of why it's such a problem) was made by Mark Gottlieb:

A puzzlemaker is creating a challenge — a mental showdown — between himself and the solver. The puzzlemaker must set himself up to lose that battle.
[emphasis his]

The problem being that puzzlers don't like to lose at mental challenges and so the needs of the puzzle are at odds with the personality of the constructor.

Secondly, and perhaps less reflective of my own personal character flaws, is the notion that the person who designed a puzzle is never (to my mind) a good judge of its difficulty. If you try to look at it from the perspective of a solver, it's nearly impossible to effectively imagine how you might solve this if you didn't already know how it works. Knowing how it works allows you to spot and interpret the clues you've left far more accurately and effectively than an actual solver may. I think of this as the Heisenberg Uncertainty Principle of Construction. You can't both know the answer to a puzzle and determine it's level of difficulty. I didn't say it was an especially apt metaphor. That's just how I think about it. Of puzzles that I've edited (most notably the NPL cryptograms page), the puzzles I've constructed are far and away the ones that come back with the most comments about how I've misjudged the difficulty. So, maybe this is just reflective of my character flaws, as well, but I don't think so.

Anyway, this is why testsolvers are such a crucially important part of the construction process. They can point out the rough edges and the steep climbs in a newly-created puzzle and help to make suggestions about how to help solvers to navigate them. But I would add that a testsolver who has examined your puzzle and offered advice on it is no longer a good candidate to comment on the revisions. See above for why.

Thirdly, solvability also requires a certain amount of debugging. Puzzles with multiple reasonable solutions are difficult to consider solvable (unless the multiple solutions are part of the point, but that generally falls under Clever). Testsolvers can help with this, but because you're only going to have so many people you can cajole into testsolving, it's generally best to try to work these problems out before you hand it off to someone else. Or, better yet, set your puzzle up in such a way as to not easily allow for alternative answers. Good crosswords don't have unchecked letters. Good cryptograms try to keep the number of letter used only once to a minimum. Cryptic clues describe the solution in two ways. Partly these are done for stylistic reasons, but there's also value to these guidelines in that they dramatically limit the ways in which multiple solutions might occur.

Finally, a truly solvable puzzle will have considered how to steer the solver back in the right direction if something goes awry. This is especially true of multi-part puzzles where the answer to one piece feeds into the next. An error in the first part will compound in the second and generally make progress any further quite difficult. Providing some means by which the solver can find their error helps to alleviate this problem. The various ways of doing this tend to be specific to the puzzle at hand, but often include the use of apropos flavortext, providing enumerations, or alphabetizing clues by solution word.

In short, Solvability is often where much of the effort of puzzle construction comes in, whereas the other categories are generally better driven by creativity, skill, style, and artistry. And that's why it's typically the most difficult to address. For me (and I imagine for most constructors), the initial idea and insight of a puzzle is the fun part of construction, along with presenting the end product to an audience. Banging away at it in the middle to make sure everything runs smoothly is just hard work.

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