Sunday, December 26, 2010

Puzzle Theory

Home on break is the only time I ever do puzzles. My dad likes puzzles, so he usually pulls one out over holidays. Given that my family's house is "desperately boring," according to my youngest brother (no video games, I think is what that means), working on a puzzle is an activity that keeps me entertained and lets me relax.

My dad and I are very similar in a lot of ways, so we both approach the problem of a puzzle from a mechanical engineer's perspective. We have what we believe to be an efficient method for completing the puzzle, so we both attack the same way. A tongue-in-cheek ode to puzzle theory:

First, go through all the pieces and separate out the edge pieces. This is a game unto itself. Sifting through all the pieces to find ones with a straight edge is incredibly tedious. The bigger the puzzle (and usually it's a 1500 piece), the smaller the fraction of pieces you are looking for, so the more monotonous it is. The reward is low - but the risk is high, because the next step is:

Second, assemble the border of the puzzle. Here is where you find out if you win Step One. Assembling the border of the puzzle should be easy. Each piece matches seamlessly to the next in line. But if you made a mistake and missed an edge piece among the giant pile of "middles", you have a break in the line, and suddenly who knows if the pieces are in the correct order. Anarchy reigns, the picture on the front of the box must be consulted - and no one likes having to consult the front of the box. It feels like cheating. But, if you have done your job in the first step, and have managed to obtain a perfect unbroken ring, you have made it to:

Third, ..... PROFIT.

Wait, no.

Third, identify distinct areas to attack. Here, against good engineering instinct, you do have to consult the instruction manual. In this case, the front of the box. The goal is to pick out areas with distinctive features - a brick road, or a bright yellow boat. Or bright yellow brick road, if the "classic movie" puzzle section was on sale when Dad was shopping... You want to pick a few suitable areas, because next you will:

Fourth, turn all pieces right-side up. As any good engineer knows, you can't work on a project if you don't know your materials. Even if your mother rolls her eyes at the takeover of most of the dining table, you should take up as much of the table as necessary to lay out all the pieces face up. Once they are face up, you can easily pick out those distinctive pieces from Step Three. Hang onto those pieces, and move right into:

Fifth, assemble distinct areas. This usually requires a mug of hot chocolate to tackle, because this is the first step requiring actual focus. (Depending on how serious you are about winning Step One, of course.) This is where you really get a feel for the soul of the puzzle. Stare into its eyes, as it were. How difficult is this going to be? How long is it taking to complete sections? Are the piece shapes distinct enough that you can easily tell "yes it fits" from "that's a no go"? Do the pieces snap together nicely, are the colors and textures clearly differentiated? Is my engineering bent so strong that I think way too hard about the merits of puzzles?

Sixth, work on vast areas. At this point you should have a border ring, with blocks of completed areas inside. Bonus if you have connected any of the block to the border. Now you are left with the vast areas. This includes things like - the sky, wheat fields, the ocean, forests of pine trees, that sort of thing. If you are lucky, you can sub-divide the vast areas. "Only-blue" sky versus "blue-with-cloud" sky pieces, if you like. If you have a wheat field, well, best of luck. At most you might hope for "waving wheat" versus "wheat-with-no-possible-distinctive-feature."

Seventh, arrange by shape. When you are down to the last areas, where no clues by color and texture are possible, it's a discouraging time. You think you are almost done (and you've even reclaimed enough of the dining table to eat from), but the last ones are the hardest. At this point, my dad and I arrange by shape. "H-shapes" have two male and two female sides, "Doubles" also have two male sides but at right angles to each other, "Triples" have three males, and "X" pieces are all female. Once arranged, it's easier  to narrow the options. After that, it's trial and error all the way to the fence. Err, end of the wheat field. Whatever. Until you finish. :)

And done!

Let me also note that there are competing methods of puzzle solving afoot in the house.

My mother prefers hunt-and-peck. She picks up a puzzle piece, and tries it in every possible open slot in the puzzle. If none work, she picks up the next piece. This is, unsurprisingly, frustrating and inefficient in the beginning stages, but quite useful to my dad and me when working on Stage Six - vast areas of wheat fields.

My sister shines most when there are "holes" left in the puzzle. When my dad and I have managed to entirely surround a spot, showing the distinct outline of the missing puzzle piece - she strikes. "Aha!" she shouts, "How could you have missed this one?" I contend that there is no glory in finding a piece that obvious. My sister contends that she merely likes to have the entire bounds of  the problem defined.

Chemical engineers, I tell you.

Any way you do it, it's still quite satisfying. Do you work on puzzles over break, internet?

Figure: Note vast area of green grass left to finish, carefully arranged pieces, mug of hot chocolate, and sister working on holes.


  1. "and no one likes having to consult the front of the box. It feels like cheating."

    but one must use all resources available! (or at least that's my excuse for constantly 'cheating')

    I propose that there is actually a step before the ones you list here, my first step in completing a puzzle happens at the store when i'm choosing the task to undertake!....

    1) The puzzle has to be "pretty" so the recruited minions are instinctively drawn to help (I see your sister fell to this trap!).

    2) Thou shalt have a puzzle exceeding 750 pieces, but not to exceed 1500. small puzzles are for weak minds who need pieces large enough to keep them from choking as they will undoubtedly swallow a few pieces while they "concentrate". Those who choose overly difficult puzzles (read: multisided, holographic, gazillion pieces, etc...) are either masochists, showoffs, or just like looking at the box on their shelf thinking "man how awesome will that be when I put that puzzle together".... but they never do.

    3) And most important! (as 3rd rules often are)
    Pick the puzzle with small, unique, and structured features! The level of detail should be proportionate to the size of each puzzle piece so that each is sufficiently unique to be placed with a +- 2 piece radius of its eventual location.

    I provide the following as a result of my optimized puzzle selection method: (the one we're putting together here at my parents place)

    I believe that example will allow me to optimize my primary puzzle metric:

    "achievement (juried score of 1.0-10.0) * (# of pieces)/ time (hours) / 1000"

    As no eligible jury member (no friends or family allowed) could be found (all the people I asked at the mall gave me the strangest look) I went ahead and rated it a 10.0, because seriously, cmon, it's awesome amIright?!

    Anyway, I guess I've wasted enough of your comment space, fell free to delete if you want :)
    Guess this is what happens when a geek on christmas break isnt busy putting a puzzle together!

    Merry Christmas

  2. Did you ever do the 3D puzzles? I had a whole stack of them, and loved putting them together and the balancing much fun! That, and the beautiful wooden jigsaws that are expensive but just so much fun - maybe we should invest in one!

  3. i think you guys are too comfortable with the classic puzzle and ready to move up to the borderless puzzle and then the solid pattern borderless puzzles. piece count puzzles have a pretty limited ceiling on difficulty. you find a methodical approach to those and you just got yourself a thesis paper


    Item weight: 28 lbs

    The gauntlet has been thrown down.