Saturday, February 26, 2005

What Is a Puzzle?

Fuldu wrote about on element of a good puzzle (Solvability), and that reminded me that I wanted to try to define what a puzzle is in general. You'd think that I'd have gotten to it sooner, since it was one of the motivating ideas behind starting this blog, but I was distracted by fiddling with the Blogger template.

On Google, the most prominent article on the subject is "What Is a Puzzle?" by Scott Kim:
My favorite definition of "puzzle" came out of a conversation with puzzle collector and longtime friend Stan Isaacs:
  1. A puzzle is fun,
  2. and it has a right answer.
I think this is a good start, but it's too limiting. The requirement that a puzzle be "fun" is not only far too subjective, it also limits the field to what could be considered "good puzzles". At the Puzzle Museum (a site that ably documents physical puzzles), there's a classification of mechanical puzzles by James Dalgety & Edward Hordern that includes a broader definition:
A PUZZLE IS A PROBLEM HAVING ONE OR MORE SPECIFIC OBJECTIVES, CONTRIVED FOR THE PRINCIPLE PURPOSE OF EXERCISING ONES INGENUITY AND/OR PATIENCE.

A MECHANICAL PUZZLE IS A PHYSICAL OBJECT COMPRISING ONE OR MORE PARTS WHICH FALLS WITHIN THE ABOVE DEFINITION.
This is closer to a definition, but there are still issues with it. For one thing, it deliberately encompasses items that are designed solely to test dexterity. For another, I am not convinced that something designed solely to exercise patience is necessarily a puzzle. The best definition I've found so far comes from "Toward a Theory of Interactive Fiction" by Nick Montfort. In the section "Puzzles and Their Solution, Montfort cites a newsgroup post by Greg Cox with two requirements:
  • a puzzle has to have an objective
  • a puzzle can't be obvious
Later, Montfort adds that a puzzle is "a challenge" with these qualities. Montfort was trying to define a puzzle in the context of Interactive Fiction, and so more qualifications will be needed, but I think this is an excellent place to start. (I'm not going to discuss IF very much in this post. If you desperately want information about it now, you might want to visit Brass Lantern.)

1. A puzzle has an achievable objective. Most definitions of a puzzle include a reference to an answer, a solution, or a goal. I like "objective" it's an adaptive word. It's a bit broader than Kim's "right answer;" it allows the possibility of multiple answers. It accepts that the point of a puzzle might be a method, not necessarily an simple answer. I think that the addition of "achievable" is a natural one. It's not necessary in the context of Montfort's original discussion, but it is in ours, where hoaxers occasional put impossible tasks into a form similar to a puzzle.

2. A puzzle is not obvious. I'm just going to quote Montfort on this, rather than try to create a shallow, just-barely-not-plagiarized version of his excellent analysis:
Obviously, there may be disagreement about what is "obvious" and what is not, but this criterion at least suggests an independent way of determining what is a puzzle and what isn't, one that does not refer to the author's intentions and the [solver]'s specific knowledge and aspirations. Any typical [solver] should be able to determine what is or isn't a puzzle simply by studying [it], without needing to interview the author or take a survey of other [solvers]. The other factors essential to the determination of "obviousness" should be not the mindset of the author or of a particular [solver], but the culture or subculture within which the work was published — along with the conventions of [the puzzle type].
3. A puzzle is a challenge from its creator. In "Toward a Theory of Interactive Fiction," Montfort draws a useful distinction between puzzles and interesting bonuses. Discussing the final puzzle in the game Adventure, he claims that the score reported by the game (349 out of 350 before solving this puzzle):
clearly presents a challenge to the interactor: to get the last lousy point, independent of successfully traversing and winning Adventure. If the interactor had 350 points beforehand and dropping the magazine gave the interactor 351 points—and there was thus no way to know beforehand that an extra point could be obtained—this could be referred to as an Easter egg but would not be a puzzle. A challenge would not have been presented initially.
This also means that a puzzle cannot occur naturally. It is always artificial, or is artificially framed. If a reporter writes an article with three instances of three words that are homonyms of each other, it's not a puzzle. But if the reporter, or another person, presents the article with the frame "Can you find nine words that sound alike in this article", it becomes part of one.

And that's all Montfort gives us. Right now, we have a definition of a puzzle that includes a game of chess: the objective is to win, it is not obvious how, and there is a challenge presented. To distinguish puzzles further, we turn to Greg Costikyan and Chris Crawford who tell us . . .

4. A puzzle is static. Both The Art of Computer Game Design by Crawford and "I Have No Words and I Must Design" by Costikyan are focused on games, and in consequence, I believe both miss the boat slightly when defining games. But a puzzle being "static" is a useful idea. Many puzzles are clearly static: paper-and-pencil puzzles are clearly so. But there are others, like Rubik's Cube or sliding-block puzzles, that are clearly reactive. And we already pulled or initial definition from an interactive medium. By "static," I mean that a puzzle must be predictable. No essential elements are subject to chance. In theory, every variable can be accounted for by the solver.

For example, in the game Deadly Rooms of Deathyou control an exterminator who must kill the creatures within a dungeon, room by room. These adversaries move according to preset rules. Those rules are not disclosed to the player, and the rules are occasionally very complex, but they are fixed. In fact, if you start from the same position in a room and duplicate a series of moves, the monsters will always respond in the same way. This game is a series of puzzles. In contrast, the "puzzle" game Tetris features randomized pieces that move at variable speeds, so that the same series of moves will produce extremely different results on different plays.

I think the definition is almost complete, but there is still a class of items that needs to be eliminated. Under this definition, Dalgety & Hordern can still claim that toys that test dexterity are puzzles, and Crawford can claim the same for simple games. So I add . . .

5. A puzzle does not test physical traits. This includes dexterity and hand-eye coordination, as well as strength, speed, stamina, height, weight, arm length and other abilities like knitting or singing in key. Any of these things might be tied into a puzzle in some way (some larger puzzle events require these kinds of things), but the puzzle is always separate from it. Many video-game puzzles feature this kind of distinction. The player may have figured out the method that kills the almost entirely invulnerable monster, but he may still be unable to actually defeat it if his hand-eye coordination is lacking.

I think this is a good working definition. It seems to filter games, toys, problems and jokes out of the category of puzzles in a way that I find appropriate. But it does leave one gray area: Trivia. I'm fine with that, for now, because I don't have a clear idea of where it ought to go. Add that to the list of things to think about for this blog.
Spoilers Ahead

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.
Spoilers Ahead

Gutter Minds

Of the first four posts to this blog, fifty percent have made reference to puzzles unsuitable for a family magazine. I don't know whether to be heartened or disturbed. (Don't say both. I don't think I want to be someone who is routinely heartened by disturbing things.)

For readers who are not members of the National Puzzlers' League (at the moment, all of the team members of this blog are), the Underground Enigma is a very irregular publication of puzzles by League members. And it is rife with sometimes aggressively lewd puzzles. It's part of a long-standing tradition. A history of the century-old League includes mention of meetings where members would give the same kind of naughty noodlers to each other in person.

The changes are often rather superficial, though. Take a look at the specifications for Jim Jenista's Banned Crosswords, and compare it to the specifications for the New York Times Crossword. They're extremely similar. And the puzzles in the Underground Enigma are identical in form to the ones in the NPL's regular magazine, The Enigma.

These publications (and other lewd puzzles) are clearly a reaction to the vague standards of decency that are applied to most widely-available puzzles. They're a statement that a puzzle can, in fact, be about anything. Just because the New York Times won't print a crossword featuring saucy puns with dirty words doesn't mean they can't exist. And, in fact, they can be very good.

Although I'm advocating adult puzzles, I'm not advocating changing the general standards of decency. They exist for the same reason that proscriptions against political bias and religious proselytizing exist in puzzles for a wide audience. A constructor lays out a path of thought for a solver, and it's common courtesy to refrain from forcing the solver to accept opinions or ideas that he is reasonably averse to. To do otherwise loses a solvers trust and usually drains the enjoyment of a puzzle.

Of course, that's only true when the audience is expected to have a diversity of opinions. If a puzzle is going to a group that is homogeneous (such as readers of a magazine with express political views), self-selected (like the people who signed up for Banned Crosswords), or very small (like the recipients of puzzles made specifically for them), then the standards change.

And it's a good thing too. Otherwise it would be a lot less fun to write puzzles for my girlfriend.
Spoilers Ahead
Among the other fun things happening at the American Crossword Puzzle Tournament, this quilt will be on display; it will later be auctioned off on E-Bay for charity.

The puzzle on the quilt itself is apparently one constructed by Will Shortz and published under the editorship of Margaret Farrar in the 1970's. I haven't solved the puzzle myself, but from the looks of the grid it would seem that before WS became the Grand Poobah of All Things Crossword at the NYT, he did have some constructing chops of his own.

Via the NYTimes forums.

-- Craig
Spoilers Ahead

Flavortext

One of the few minuses to this year's Mystery Hunt was a surprising lack of flavortext. A few puzzles here and there offered up some minimalist flavortext, but nothing like in years past. I understand the objections that Setec Astronomy posted in their livejournal blog, but disagree with the overall condemnation.

My own philosophy towards flavortext is that:

A) It should convey part of the story behind the puzzle, whether it's an independent puzzle or part of a larger set. Certainly Ucaoimhu's cryptics (such as Underground Enigma 3 cryptic "F***, It's a Cryptic") could be introduced much more succinctly, but the background provided more of a raison d'etre to the puzzle, a more pronounced sense of involvement with the theme. Well-written flavortext, like any writing, should engross the reader without presenting the reader with tangents and distractions.
B) It should confirm "a-ha"'s or provide additional cluing, but not be the only source of cluing. An otherwise excellent idea for a puzzle involving cliches from the 2004 MITMH was hampered by the reliance of the reference to the Prophet's Birthday as an indicator to take certain words. This is way too indirect, mostly because lengthy flavortext can lead solvers in untold different directions.
C) If it is the only source of cluing, make it short and sweet. An excellent 2003 MITMH involving an Etch-a-Sketch and opposites clearly indicated in the flavortext that opposites were part of the puzzle.

Flavortext doesn't have to clue at all however. It can provide a thematic backdrop for the puzzle, and again drop hints, but it shouldn't distract the solver, or rely on those hints for solving purposes.

Thoughts?
Spoilers Ahead

Thursday, February 24, 2005

The puzzle "groove"

One of the things that sometimes intrigues me as a puzzle constructor is how the creative process involved in creating puzzles is very much a product of not only who I am (background, interests, and tastes), but also whatever state I happen to be in. If I'm "in the groove", things go well; if I'm not, I might as well go watch TV, or trim my toenails, or whatever. I think one of the reasons things work this way for me is because for me, puzzle construction involves a type of focussed play. Sometimes my current state affects my ability to engage in this focussed play, in which case my ability to construct is also affected.

Today was a rather extreme example of this. I had my puzzle binder with me in my satchel on the bus, and I was able to construct quite happily and productively on both the half-hour bus trip to work and the trip back home. (You might laugh, but it's usually relatively quiet, and for the most part the trip lacks interruptions or distractions.) I had planned to work on something else construction-wise after supper - the crossword puzzle for my almost-monthly regular crossword gig - but the people I share my house with were tired and cranky (and one was not feeling well either) and there was a modest amount of tension in the air for a little while. I tend to pick up on other people's tension very easily, and tonight was no exception. Sure enough, I lost the relaxed state I had achieved earlier in the evening, and the evening was a washout from a constructing perspective, even though I had been constructing productively just an hour or two earlier.

Another side effect of this is that the more I'm in the puzzle-constructing groove, the more I tune other things out, and that includes people. Fortunately, my housemates are very good about this, but I do have to be careful about not ignoring other people (like my girlfriend).

-- Craig K.
Spoilers Ahead

Teeny Tiny News Tidbit

For those of you who pre-ordered the Banned Crosswords book that was being pre-sold at the American Crossword Puzzle Tournament in Stamford last year, the preordered books have just been mailed out on Wednesday, February 23rd.

(Via the NYTimes forums.)

--Craig K.
Spoilers Ahead

Origin

In my personal blog, I wrote (vaguely) about creating a blog about puzzles. This is it. The mission statement is on the main page:
A group effort exploring the design and aesthetics of puzzles from the points of view of creators and solvers.
Of course, I'm the entirety of the group, right now, but that should change shortly.

My goal, right now, is to start a discussion about what puzzles are, how creators and solvers approach them, what makes them good or bad, what makes them clean or broken, and what makes them fun or excruciating. The scope of puzzles will be wide. This blog won't focus only on crossword puzzles or pencil-and-paper puzzles. Puzzles of all sorts, including logic puzzles, video-game puzzles, mechanical puzzles, etc. will be included.

In doing all this, the blog will try to keep readers linked to puzzle content on the Web; it will also try to stay up to date with non-Internet puzzles too. And because the people who work (or will work) here have other interests, you can expect to find occasional diversions into games, trivia, language, math, and other areas.

So, welcome. Let's see if this can stay afloat until July.
Spoilers Ahead