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August 23, 2010

The Cruciatus Curse

Each year, we begin the planning process for the Microsoft Intern Puzzleday in the same way, with an evening of training in puzzle design. This is primarily aimed at the folks who've never helped put on such an event before, but it's a good refresher for everyone. The best part, though, comes after our training lead, Kenny Young, works through his PowerPoint slides. At that point, we break up the group into smaller sections of 5-8 people each, and each section does some slightly directed brainstorming on puzzle ideas. Not only does this help the newbies get a sense of how the process works, and provides a safe environment for tossing out ideas, but we often get three or four puzzles from this that survive all the way to the final event.

I said "slightly directed" brainstorming, and that describes it pretty well. Each section gets a brief visit from Kenny, who imparts a little germ of an idea to kick things off. My first year, the theme of the event was to be Hogwarts, the school for wizards from the Harry Potter books. Kenny came to our section and looked a little sheepish.

"Um, this is going to be pretty sketchy, even moreso than usual; I'm sorry about that, but I'm also sure you'll be able to do something with it."

Oh goodie, I thought; this should be good.

"OK, Hogwarts is in England, right? Well, I've noticed that the British seem to have a lot of interesting pairs of things. For example, Marks & Spencer, the department store in London. Or bangers and mash, which is apparently something you can eat. Got it?"

We all stared at him.

"Well, that's it. Go for it!" And then he left, presumably to go torture the next section, too.

As I said, the brainstorming is only "slightly" directed.

As a kind of temporizing maneuver, we first spent some time trying to come up with a bunch more such "pairs". After a while of that, the ideas started flowing for how to make use of them. Over the course of the next half hour or so, we played around with a lot of ideas, but just one of them had any staying power, and Cruciatus Curse was the result. The actual detailed puzzle design work was a collaboration between me and Stacey Eck, but we probably wouldn't have gotten that far without all of the ideas flowing around that initial brainstorming session.

The answer to Cruciatus Curse, like all of the puzzles in Puzzleday, is a single word or short phrase.

Well, that's it. Go for it!

August 21, 2010

The Calibron 12-Block Puzzle

In March of 1931, a man named Theodore Edison, younger son of the famous inventor Thomas Alva Edison, filed articles of incorporation for a company named Calibron Products in West Orange, New Jersey. The company's first product was a special kind of graph paper, designed to make it easier to create perspective drawings.

But in December of the next year, the company filed for a copyright on "The Calibron 12-Block Puzzle". An advertisement for the puzzle appeared a few years later, in the January 1935 issue of Popular Science magazine.

The instructions for the puzzle read, in part, "The problem is to arrange the twelve blocks to form a single large rectangle. Any rectangle will do, provided that all twelve blocks are used... We guarantee that there is a straightforward, accurate solution of this puzzle in a single plane, and without recourse to any kind of trick... However, in spite of the enormous number of possibilities, there appears to be only one basic arrangement which satisfies the above conditions... We once offered $25 for the first solution of this problem and distributed hundreds of puzzles at that time, but received almost no correct arrangements! We should like to hear from you if you succeed in making the rectangle unaided."

Not very many people have copies of the original Calibron 12-Block Puzzle, and that bothered a good customer of mine, who wrote me earlier this year asking for advice on how to get a few copies of the puzzle made. I decided to make the copies for him myself, and once the first prototype came off the laser cutter, I decided that it was quite an intriguing design, and that I'd like to make it more widely available again.

The twelve rectangles making up the puzzle have very promising dimensions, with lots of obvious interrelationships that lead you to think that won't have too much trouble getting them to fit together in nice ways, and that's true, as far as it goes. However, "as far as it goes" isn't likely to be as far as actually solving the puzzle unless you put in some time and concentration. This is one of those very attractive puzzles that just won't yield without a bit of a fight.

With modern computers, it was straightforward to verify the original marketing claim: there is, indeed, a unique solution to the puzzle. I think you'll enjoy torturing your friends as they try to find it.

Square Dance

Take a 2x2 square, and join it to another 2x2 square, but only by half an edge. There's only one way to do that (ignoring reflections and rotations), shown below:

Now join on a third 2x2 square, again by only half an edge. This time, there are just four possibilities, all seen in the photograph below.

Back in 2002, my good friend Derrick Schneider noticed this nice little set of slightly strange shapes and wondered whether or not they'd make a good puzzle. He whipped up a little program to try packing the pieces into an 8x8 tray. To his delight (and later ours), there was just one way to fit in all four pieces! Many designers would have stopped there, but for some reason Derrick also tried running the program on a 7x9 rectangle: once again, incredibly, there was a unique solution!

Imagine the fun: he comes up with a simple way to define a set of pieces, the resulting set is nice and small, and that set fills both of the two most obvious tray shapes in unique ways. Believe me, such a mathematically elegant puzzle design doesn't come about every day! Add to that, the resulting puzzle falls into a real sweet spot of difficulty: harder than you might guess (those pieces are just plain tricky to get your brain around, especially the curled-up one), but easy enough to yield to a little patience.

Perhaps that explains why, when Derrick presented his puzzle at the 22nd annual International Puzzle Party, the jury for the Puzzle Design Competition awarded it an Honorable Mention, one of just three puzzles so honored.

Now, for the first time in many years, I'm happy to make Derrick's wonderful little puzzle available for sale again. Initially, I'll be selling off the remainder of Derrick's original manufacturing run; the last time I visited, I got him to dig around in the basement and pull out all of his old inventory for me. After that limited supply sells out (he could only find about 15 of them), I'll start making my own copies for you. This is simply too good a puzzle to remain unavailable for so long.

Update: Square Dance is now also available in this economical CD jewel-case edition! (Note: your tray and piece colors are likely to differ from what's shown in this photo. We use a wide variety of colors and every puzzle is made from a different pleasing assortment.)

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