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:

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.


This post, along with Craig's comments in Foggy's Flavortext post, reminded me of something I had thought might be useful for this blog. A glossary of unusual terms, less for cogent definitions like the above and more for acronyms, coined words, and odd usages, would probably be a good idea. We've already needed to explain NPL, UE3, noms, and flavortext, among others. I imagine there will come a time when dictionaries come into discussion, and I'm always momentarily taken aback when the person I'm speaking with doesn't understand what 11C or NI3 means. Having one repository for these definitions would mean less repeated explanation for those who are familiar with the jargon and ease of access for those who aren't.

By Blogger Fuldu, at 11:13 AM  

Before we start making crib notes for ourselves, I think we should just pay more attention to how we introduce jargon and terms of art. Jargon can usually be dispensed with (for example, I always call Merriam-Webster's dictionaries by their full names when I'm not talking to NPLers), and the terms of art will arise as we go along. Ideally, I'd love any Puzzle Can(n)on glossary to be a set of links to Puzzle Can(n)on posts that arose naturally.

By Blogger Tablesaw, at 11:48 AM  

Tablesaw, I think your first point on the definition of a puzzle, that it has an “achievable objective,” is a valid defining quality, but also addresses the appeal of the puzzle in contemporary culture. In "Small is Beautiful: Economics as if People Mattered," E.F. Schumacher references the concepts of “divergence” and “convergence” put forward by G.N.M Tyrell. Divergent problems are ones that “have to be lived and can only be solved in death” while convergent ones are “created by a process of abstraction.” Divergence provides for the perpetuation of community, industry, and culture because it is designed to never end. Convergence, Schumacher argues, is a practical invention that serves the human psychological need for closure.

"A busy detective who has been dealing with divergent problems all day long will read a detective story or solve a crossword puzzle on his journey home. He has been using his brain all day; why does he go on using it? The answer is that the detective story and the crossword puzzle present convergent problems, and that is the relaxation."

Some people are attracted to puzzles with a predictable form, such as the crossword, while other are intrigued by puzzles with unknown structures, such as the MIT Mystery Hunt, but in both cases the solver carries an initial expectation that the problem will challenge mental facilities while eventually coming to an end. In an intellectual sense, those are qualities one would use to recognize the problem as a “puzzle,” but on a subconscious psychological level, those are qualities that one could use to identify the problem as therapy.

By Blogger tmcay, at 6:12 PM  

For #5, I don't think you want your restriction to be negative (saying what a puzzle doesn't test). Puzzles also don't test emotional traits or psychic traits. It seems it would be more to the point just to say it's a test or challenge of the intellect.

By Anonymous Anonymous, at 9:49 AM  


I used a negative definition because it seemed a more natural. I like the word "intellect" (which didn't occur to me at the time), but I don't know precisely how to section off some parts of the mental realm and not others. For example, I'm unclear about how memory fits into things. The negative definition effictively screened out every concrete example I could think of, while leaving in everything I could think of.

As for tests of emotional and psychic traits, I can't conceive of how they would be structured so that they also meet the other qualifications. I'd love to be proven wrong, though.

By Blogger Tablesaw, at 5:28 AM  

I think you need to be a little clearer when you say "a puzzle is static".

It's possible for feedback for a static puzzle to be received via a random mechanic; take, for example, Petals Around the Rose. The internals of the puzzle are consistent, of course, but I believe many people might take the rolling of dice to be part of the puzzle.

By Blogger Jason Dyer, at 9:40 PM  

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