Pavel's Puzzle Blog

A Holiday Discount Puzzle

Solve this puzzle for 10% off any order!

Well, this is the third year in a row for the Holiday Discount Puzzle, so I guess now it's officially an Annual Tradition around here!

For those of you just joining us this year, in honor of the holiday season, I've created a puzzle that you can solve to earn a discount on any order here at Pavel's Puzzles. To get started discovering the 2012 holiday discount code, cut out the eight squarish pieces linked to by the image below. Arrange them in the eight positions in the diagram also shown there, without overlapping, such that some of the heavy black lines form a complete diamond shape; some other lines will stick out in various places. The letters on the pieces must remain right-side up.

There is only one solution to this challenge. Once you’ve found it, I’m sure you’ll have no trouble at all figuring out the holiday discount code. To use it, make any order at http://www.pavelspuzzles.com and enter the code in the “instructions to merchant” space at PayPal. When I get the order, I’ll issue you a refund for 10% of your order amount (excluding tax and shipping). Even better, you get that same discount for every order you make before the end of 2012!

Continuing to follow tradition, I've just released a whole bunch of new puzzles on the website for your holiday shopping excitement:

Any good mason knows: when laying bricks, you don't want the cracks in one row to line up with those in other rows. Can you satisfy The Bricklayer's Challenge, or will you end up banging your head against this wall? Mathematician and writer Barry Cipra showed off a huge wooden version of this at the Gathering for Gardner last Spring, and now I've brought a more portable, and more colorful, version to the website!

At first, Trail and Error seems to be just a little jigsaw puzzle, and it is, but it's a tricky one, and that's just the beginning of the solving experience! My 10½-year-old nephew handily solved his version of this one; can you do as well with yours? This puzzle is especially great for that jigsaw fan on your list that you'd like to push just a little ways off their well-worn trail.

What if you left some beer bottles out in the sun too long, and they melted and slumped all over each other? And what if you could take that pile apart and put it together again? Each Dali Bottles puzzle sculpture is custom-made for you from real beer bottles by Oregon glass artisan Sarah Gage-Hunt. It will baffle and intrigue your guests for a long time to come!

I've discovered that I really enjoy creating custom-designed jigsaw puzzles, and now I'm officially bringing that offering to Pavel's Puzzles! I'll use your photograph or other design and I'll work with you to incorporate a set of 'special' representational pieces to make your puzzle a one-of-a-kind delight for the intended recipient!

Of course, I still offer all of my earlier designs, too. My holiday discount puzzle is a perfect way to satisfy (or frustrate) that puzzling person on your gift list while saving a little cash at the same time. Just imagine the look on their face when they find one of these puzzles in their stocking!

Posted by Pavel at 06:32 PM | Permalink | Comments (0)

As I've described elsewhere, I've taken to creating personalized puzzles for my young niece and nephew on their birthdays and at Christmas. The first puzzle I designed for my niece was for her fourth birthday. Of course, I tried to take it easy on her: no multi-stage complications, no difficult mechanical gyrations, and no Japanese logic grids. It was just a simple little 36-piece jigsaw puzzle of a photograph showing her and her brother smiling together. (As those of you who are parents already know, 36 pieces is too many for a four-year-old, but she had fun anyway, putting it together with the help of the rest of her family.)

Making that first jigsaw, though, made a lasting impression on me: I really enjoyed laying out all of the piece boundaries, trying to break up (or avoid breaking up) color regions, and looking for a clean, balanced distribution of cuts. Later that year, when I made another jigsaw for her brother for Christmas (that later inspired my puzzle Trail and Error), I got another jolt of that jigsaw-making magic sauce, and then I was well and truly hooked.

With several more jigsaws under my belt, I'm now ready to take the next step: offering to make a custom jigsaw puzzle just for you!

My jigsaws are laser-etched and laser-cut from heavy, 3/16" acrylic, giving them a sturdy, high-quality construction that means they'll stand up to lots of handling and remain crisp and clean for many, many years. Because they're etched, not printed, the design absolutely won't rub off or fade. It also means, though, that I can't do full-color imagery; the acrylic sheet will be one color and the etched areas will be whitened more or less based on the intensity of the laser. What that means, essentially, is that I can reproduce black-and-white photographs, line art, woodcuts, and other such monochrome designs. The highest contrast comes from using black acrylic, but many other bright colors can work well, too.

I can vary the number and the size of the pieces to your taste, from as few as a dozen pieces, say for a young child, up to a few hundred pieces, if you're looking for something more epic. Similarly, the difficulty of the puzzle is up to you: if you like, I can turn out a really nasty set of cuts and an irregular outside edge that should satisfy the most demanding of solvers, or I can give you a pleasant half hour of solving with a few friends. It's up to you!

One of my favorite things to design into a jigsaw is 'specials', pieces in representational shapes that either reflect the subject matter of the imagery or refer to the personality or history of the intended recipient. For example, as seen to the right, in a puzzle celebrating the release of Rachel Hartman's novel Seraphina, I included several musical instruments (reflecting a major theme of the book), Rachel's initials (traced from her own calligraphy on an earlier book cover), and the profiles of two characters from a comic book that Rachel had produced many years earlier. The specials can be whatever shapes you like, whatever it takes to make your custom puzzle truly 'special' to you!

Of course, the cost of a custom puzzle like this is going to vary a lot, depending on just what you're asking me to produce, but here are a few starting points to give you a sense of things:

• about 20 large pieces, including the letters of your child's name in a contrasting color, about 11 inches square, where the design is a simple maze of birthday balloons spelling out "Happy Birthday": $75
• about 40 pieces, 11 inches square, black and white photograph or other monochrome design provided by you, no 'special' pieces: $75
• same puzzle with four custom 'special' pieces: $115
• about 100 pieces, 11 by 18 inches, eight 'special' pieces: $200
• same puzzle, with about 200 pieces and 12 'special' pieces: $350

In all cases, these prices are for the first copy. If you'd like multiple copies of exactly the same design, the additional copies would be $30 to $60 each, depending on the size and number of pieces.

Does this sound intriguing to you? Wouldn't this make a great birthday or holiday present, or maybe a unique promotional item for your business? Please get in touch with me at pavel@pavelspuzzles.com and let's start talking about how I can make a very special puzzle, just for you!

Posted by Pavel at 04:03 PM | Permalink | Comments (0)

Many years ago, while visiting some friends in Port Townsend, Washington, I came across a very unusual disassemblable sculpture, made from about 9 or 10 pieces of bronze. Each piece looked like a molten metal droplet, conforming to the shapes of the pieces underneath it. It looked like the maker had dropped a bit of molten bronze into a small cylinder, let that cool, then dropped another molten bit partially on top of that one, let it cool again, and then repeated this process, droplet by droplet, until he'd built up a little tower of droplets inside the cylinder. By some alchemical magic, none of the droplets had stuck to the cylinder or to each other, so you could lift off each droplet again in turn, effectively reversing the process of its creation.

As a sculpture, it was fascinating, and as a puzzle, it was wonderful. Each time you added a piece to the growing tower, it locked itself into place with an incredibly satisfying 'click'. It was an addicting combination: heavy, organic, natural shapes that felt great in your hands, then interlocking and conforming to one another so tightly as you assembled them together. Obviously, I bought the one they had there in the shop. (I can't seem to lay my hands on that puzzle just now to take a photo of it, but you can see a few other examples here and here.)

Several years later, I spent some time tracking down the maker, calling every gift shop in Port Townsend until one recognized my description of the sculpture and put me in touch with Steve Johnson, the owner of a metal foundry there who'd created and sold the sculptures under the brand name Paracelsus Puzzles. You may have noticed that I used the past tense there. I discovered in my conversation with Steve that he'd long since stopped making the puzzles and gone back to normal metal-foundry work; puzzle people had apparently proven too demanding, always asking for new designs, and he'd eventually just gotten tired of it. Worse, he'd never revealed or licensed his magical don't-stick technique to anyone, so nobody else could make them either!

I was disappointed, of course, but it occurred to me that I was living in the Puget Sound area, the land of Dale Chihuly and the Glass Museum. There are tons of great glass artisans around the greater Seattle region; surely I could convince one of them to work with me to replicate something of the feel of those metal puzzles in heavy art glass! Sadly, though, every time I brought up the idea with glassblowers, here and elsewhere, they looked at me like I was crazy, or at least naïve. They would always patiently explain that, if you get glass hot enough to melt and run like that, there isn't anything you can do to keep it from sticking to any other glass it touches. After a while, I gave up on my little dream and stopped asking.

A few years ago, though, my wife and I were driving down the Oregon coast, and we stopped in to visit an old college friend of mine, Sarah Gage-Hunt, whom I hadn't seen for some 25 years. I discovered that, in addition to teaching high-school math, she had become a fused-glass artist, heating carefully arranged bits of glass in a kiln to melt them together into beautiful dishes, platters, and sculptures. I couldn't resist bringing up the puzzle-sculpture idea, just one more time, and to my delighted surprise she said, "Oh, sure. We can do that. No problem." After I got over my shock, we spent pretty much the rest of our visit talking about techniques and sculpture ideas, until our respective spouses got thoroughly tired of it and made us stop.

It's taken a while to refine our ideas and techniques, but we're finally ready to bring our first offering to you, the puzzle-buying public: we call it Dali Bottles. Each sculpture is made from a dozen real beer bottles, plucked from certain doom in the recycling bin. Sarah first melts each bottle separately in the kiln overnight, flattening it like all of the air has gone out of it. Then she stacks all twelve bottles up in a random, circular arrangement and runs that though the kiln one final time. The bottles in the stack slump over and hang on one another like the watches in that famous Salvador Dali painting, each conforming so tightly to the ones beneath it that there's literally no space left at all. When you're putting the stack back together, you will have no doubt whatsoever when you get one into the correct position: it 'clicks' into place so strongly, so surprisingly, and just so satisfyingly that you'll find it impossible not to smile. Really, folks: I cannot convey to you clearly enough how truly wonderful that feels.

We've decided to start by offering two versions of Dali Bottles. One is made from brown bottles, and it's a little bit cheaper, partly because that's the kind of beer that Sarah's husband prefers, and partly because it's easy to clean up those bottles, remove the labels, and get them ready for the kiln. The other version is made from your choice of clear, green, or blue bottles, or from any combination of the four colors that you like; this version requires more work on Sarah's part, finding and preparing the bottles, so we're charging just a bit more for it.

Obviously, every Dali Bottles puzzle is completely unique, and we're making them to order, entirely on demand, so it'll take a little while to make it and get it into the mail to you. Count on at least a week to create the sculpture itself, possibly more depending on current demand, and then some more time to pack it up safely for shipping. Be assured though, you're getting something very special: a hand-made, one-of-a-kind puzzle, artwork, and conversation piece that you'll be showing off and enjoying for years to come.

Posted by Pavel at 05:50 PM | Permalink | Comments (0)

One great thing about being an uncle, as opposed to a parent, is that you have a societally acknowledged right to spoil your nieces and nephews. Personally, I take that right a step further: I believe that it is my obligation to fill in any holes I see in the rearing environment provided by my sister and her spouse for their children. Specifically, I see it as my role to corrup—I mean, indoctrinate—my niece and nephew into the world of puzzles.

(Admit it: you're surprised, aren't you? No? Oh, well, never mind that then.)

I think I started in on my nephew when he was only eight or nine years old, making a couple of small pencil-and-paper puzzles for his birthday that led to some kind of a silly metapuzzle answer. For his tenth birthday, I stepped it up a bit to a sequence of four puzzles, each unlocking the next, leading to him finding his real present, hidden somewhere around his house. He's 11½ as I type this, and I'm already planning something even more involved for his twelfth...

I tell you all of this because my nephew was the original inspiration for this puzzle. For his Christmas present last year, I wanted to try my hand at creating a jigsaw puzzle. Of course, I couldn't just leave it at that, could I? No, I had to make it one of my multi-stage puzzles: after he'd solved the jigsaw, there would be a new puzzle revealed, and that would lead to yet another puzzle, until he finally got a satisfying answer. The version I made for him led to a final message that was very silly indeed, and very specific to him; it was his present, after all.

After Christmas, though, I got to thinking that the main ideas in his puzzle were good enough that I should really use them again in a puzzle for the website. Some months later, I finally got around to creating the puzzle you see here, and testing has shown that it works pretty well. It's a real jigsaw puzzle, and not a trivial one, but also not a huge one; it's only 64 pieces, but take my word for it: it'll still keep you busy for a little while. And, of course, that's just the beginning of the solving experience! I won't even tell you how many layers of additional puzzle there are after assembling the jigsaw; not only would it spoil some of the surprise, but it's actually a little tricky to count them!

(By the way, the puzzle's name isn't a typo; believe me, you'll understand why by the time you finish this one...)

So the question comes down to this: my 10½-year-old nephew handily solved his version of this puzzle; can you do as well with yours?

Posted by Pavel at 10:25 PM | Permalink | Comments (0)

This Spring, I once again attended the Gathering for Gardner, that eclectic (or is that eccentric?) conference bringing together mathematicians, puzzlers, and stage magicians for talks, conversation, demonstrations, and fun. One thing that particularly caught my eye this year was a large, beautiful, wooden tray puzzle that the mathematician and writer Barry Cipra was showing off. You can see my snapshot of it to the right.

As any good mason knows, when you're laying courses of bricks, you want to avoid having the cracks between bricks in one row lining up with the cracks in other rows: aligned cracks tend to make the wall weaker. This puzzle puts you in the role of a bricklayer with very high standards indeed: you must arrange the bricks such that no crack in one row lines up with a crack in any other row!

After playing with Barry's puzzle for a little while, I knew that I wanted to make my own version of it.

Then, to give the solving experience a little more texture, I wrote some software to help me craft a set of increasingly difficult challenges. The first is just to lay out the pieces as I described above, and there are 2,184 solutions to that. The next challenge is to find a solution that has 180° symmetry, one where the solution looks the same after you turn it upside down (other than the colors, of course); there are only 56 solutions to that one. The third challenge is to ignore that symmetry idea and, instead, to find a solution where no two pieces of the same size (4 units or less) overlap each other vertically; that takes us down to just 5 solutions. Finally, you have to find a solution that obeys both of those last two constraints: 180° symmetry and no same-size overlaps. That final challenge has (wait for it...) exactly one solution.

What I particularly like about this puzzle is that it spans a nice range of difficulty: the first challenge should yield to anyone who puts any patience into it, but solving all four challenges should keep most solvers busy for a nice little while...

Posted by Pavel at 10:13 PM | Permalink | Comments (0)

A Holiday Discount Puzzle

Solve this puzzle for 10% off any order!

I had so much fun with last year's holiday-discount-puzzle promotion that I've decided to do it again! Who knows, maybe it'll turn into an annual tradition around here...

Just like last year, in honor of the holiday season, I've created a puzzle that you can solve to earn a discount on any order here at Pavel's Puzzles. Simply cut out the fourteen strips linked to by the image below, cutting along the heavy lines. Then weave them together into a square with seven strips placed horizontally and seven placed vertically, such that you can see all of the letters. (Ignore the orientations of the letters. I've scrambled them to avoid giving you too much information. Heh.) Finally, read out the message to learn the secret discount code!

Once you know the answer, make any order at Pavel's Puzzles and type the answer into the "Instructions to Seller" space on the PayPal checkout form. When I get the order, I'll issue you a refund for 10% of the cost of your order! (Sales tax and/or shipping excluded.) Even better, you can get the same discount on as many orders as you like between now and the end of this year!

To further spur you into action, I've just released three new puzzle designs:

Edgewise is just a simple little jigsaw puzzle, isn't it? With only a couple dozen pieces or so, how difficult could it be? This was my Exchange puzzle at the International Puzzle Party in Berlin this summer, and it's the latest in my series of multi-stage solving experiences, sure to keep your mind occupied for a little while.

World-renowned computer scientist Donald Knuth conceived of this puzzle a few years ago and I've designed this elegant physical realization of his five progressively more difficult challenges: can you fit the pieces into the tray such that the Tromino Trails form a single continuous loop? Each challenge has a unique solution and helps ‘train’ you to be ready to take on the next one.

This big, icy beauty is perfect for those coming winter nights in front of a fire. Icicle Jam was inspired by the startlingly blue ice of Alaskan glaciers and once you've assembled it you'll have a display piece that will be a striking addition to any room. Of course, first you'll have to survive its jagged interlocking challenge. Dress in layers, and make sure someone knows where you've gone!

Of course, I still offer all of my earlier designs, too. My holiday discount puzzle is a perfect way to satisfy (or frustrate) that puzzling person on your gift list while saving a little cash at the same time. Just imagine the look on their face when they find one of these puzzles in their stocking!

Posted by Pavel at 06:18 PM | Permalink | Comments (0)

One of my best-selling puzzles is the Finnish Cross (formerly known as Six Tabbed Planks), designed by Matti Linkola. That might be simply because it's one of the least expensive puzzles on the website, but I prefer to think that it's because it has a compact elegance about it that makes it fit well on a executive's desk or anywhere else. I have received one or two letters about it, though, from purchasers who were disappointed at its overall size (about two inches cubed).

In its pure form, though, the puzzle has a certain fixed aspect ratio: if I made one twice as large, it would necessarily be made from plastic that was twice as thick (1/2 inch instead of 1/4 inch). It's a slow and tedious process to laser cut such thick acrylic, and some artifacts of the cutting process get magnified as well.

For example, the laser doesn't cut a channel that's at a perfect right angle to the surface; the channel is more V-shaped, wider on the 'entry' side and narrower on the 'exit' side, so the pieces end up being slightly trapezoidal in cross section rather than rectangular. Now, proper laser-cutting technique can significantly mitigate such tendencies, but as you scale up to thicker and thicker materials, the artifacts start to overwhelm the mitigations. For a 3D interlocking puzzle like the Finnish Cross, the result wouldn't be as satisfying as I'd like.

One morning, as I pondered this 'size matters' issue, I idly noted that I had managed to build up a small inventory of fluorescent blue acrylic, originally intended for use on a commission where we ended up going in a different direction. That plastic had always put me in mind of the shockingly blue ice we'd seen on Alaskan glaciers, and now that led me to picture a version of the Finnish Cross that looked like a whole bunch of icicles had been jammed together into a kind of starry, snowflakey shape. The idea really appealed to me, and I immediately sat down with my drawing software. A few hours of design later, I was ready to try cutting out the first prototype for Icicle Jam, and the result was just as striking as I'd imagined.

This jagged, icy beauty is big, about 6-1/2 inches in diameter, and really eye-catching in any setting. The internal interlocking configuration is the same as in the Finnish Cross, but I find it's a little bit tougher to visualize it in this new, more flamboyant form, making for a slightly more difficult solving experience. If you're looking for a satisfying puzzle that will really remind you of its sub-Arctic roots, Icicle Jam may be just the ticket!

Posted by Pavel at 03:37 PM | Permalink | Comments (0)

In the summer of 2009, at the annual International Puzzle Party, we were treated to a talk by the justly renowned computer scientist, mathematician, and author (and all-around Really Nice Guy™) Donald Knuth. He spoke about some of his favorite puzzles and some new puzzle ideas he'd been working on. As part of the presentation, he passed out a sheet of paper with several puzzles on it for us to solve later.

One of the entries on the paper was a description of an interesting set of twelve trominoes (aka triominoes), pieces made up of three unit squares joined in a little 'L' shape. Each piece had a line drawn on it (on both sides, so you could flip the pieces over), and your goal was to arrange them into a six-by-six square such that all of the lines formed a single, unbroken loop The solution, he said, was unique. OK, fun enough, but Don wasn't through, not by a long shot.

Then, he listed four more similar trominoes and said that, if you added those new pieces to the original ones, you could arrange them all into an eight-by-six rectangle, with the lines again forming a single continuous loop, and again the solution was unique. This was sounding even better, but he kept going!

Next, Don showed two more trominoes to add in, now enabling you to build a unique nine-by-six rectangle with the same properties. That was followed by yet two more trominoes, now forming a unique ten-by-six rectangle!

Finally, he showed four more tominoes you could add to everything that had gone before, with the entire set now making a nine-by-eight rectangle, still with the lines forming a single continuous loop, and still with a unique solution!

Five separate, progressively more difficult challenges, all from the same set of simple-seeming pieces, all with unique solutions: this was great, an elegant puzzle construction! There was only one teensy-tiny little problem: Don hadn't actually given us the puzzle! All we had was a description of the puzzle, stuck on this sheet of paper!

I immediately resolved to design a nice physical packaging of Don's puzzle idea, with all five challenges and all twenty-four tromino pieces included, along with a simple way to remember which pieces went with each challenge. The result is Tromino Trails. The initial six-by-six challenge isn't trivial, but also isn't particularly difficult. After that, each challenge poses a progressively tougher problem but also trains you, in a sense, to be ready for the challenge that follows.

My friend Stan Isaacs used this as his Exchange puzzle at this summer's International Puzzle Party in Berlin, and now I can make it available more broadly. I think it provides a very satisfying puzzle experience that's accessible to and enjoyable by both experts and new puzzlers alike.

Posted by Pavel at 02:43 PM | Permalink | Comments (0)

A couple of years ago, I was privileged to be commissioned to produce a unique, custom puzzle for the 2009 Science Foo Camp, a eclectic annual gathering of scientists sponsored by the journal Nature, by Google, and by O'Reilly Media. I ended up producing 300 copies of a special version of my then-new puzzle Anansi's Maze, which they then handed out to all of the attendees that summer. I was also invited to attend the event myself, which was truly wonderful, and they asked me back again the next summer. At the event in 2010, I started discussing with the organizers the possibility of my producing another puzzle for them for the 2011 gathering, this time a puzzle that had been designed from the beginning specifically with that event in mind.

I spent some time brainstorming puzzle themes with Kay Thaney from Nature, and we hit upon what I thought was a great inspiration. Tim O'Reilly, the founder of O'Reilly Media and one of the organizers of the event, has a favorite saying that he brings up at the introductory session of each Foo Camp:

When Tim says this, he's referring to the edges between intellectual disciplines, and how Foo Camp is designed to bring together people from different areas and enable a kind of creative friction as the areas butt up against one another.

When we brought up the saying in our puzzle-theme brainstorming, however, it immediately took on an entirely different meaning for me, and my mind began chewing over all sorts of ideas for embodying that meaning in a puzzle design. Edgewise is the result of that chewing. (Hm. That sounded better in my head than it reads here. Oh, well...)

Edgewise consists of about two dozen jigsaw-puzzle pieces, most with large letters etched on them, and some with additional words of potential significance. As this is the latest in my series of multi-stage puzzles, I won't say anything more about the solving experience here, but I can tell you that it should keep you happily busy for a little while as you make your way through it.

In the end, ironically, Edgewise did not wind up being used as a Science Foo Camp gift, but I remain grateful to Tim and Kay for providing the inspiration for this puzzle. We did use it in this summer's Microsoft Intern Puzzleday event, and I also used it for my Exchange puzzle at the International Puzzle Party in Berlin, so I think it's getting the kind of exposure it deserves, particularly because now it's available here on the website for you to try out for yourself!

Posted by Pavel at 02:43 PM | Permalink | Comments (0)

A Holiday Discount Puzzle

Solve this puzzle for 10% off any order!

In honor of the holiday season, I've created a puzzle that you can solve to earn a discount on any order here at Pavel's Puzzles. Simply cut out the pieces below and assemble them into the shape shown; then find the clues to the one-word final answer. (Ignore any words shorter than four letters.) The final answer is just three letters long (or five, depending on which form you prefer).

Once you know the answer, make any order here and type the answer into the "Instructions to Seller" space on the PayPal checkout form. When I get the order, I'll issue you a refund for 10% of the cost of your order! (Sales tax and/or shipping excluded.) Even better, you can get the same discount on as many orders as you like between now and the end of this year!

To further entice you, I've just released two new puzzle designs:

This puzzle is shaped like a magnifying glass, but the glass has been broken! Reassemble the glass in two different ways to reveal clues to a mystery! "Get a Clue!" was my Exchange puzzle at this summer's International Puzzle Party in Japan, and I've finally finished the minor revisions I wanted to make before releasing it on the website.

Easy Eight / Hard Eight is a lovely little tray puzzle designed by my friend Bob Hearn: just pack the letters of the word "EIGHT" into each side of the tray. The "easy" side isn't too tricky, but the "hard" side will keep you busy for a while...

These two join two more new designs I released late this summer:

In Derrick Schneider's Square Dance puzzle, there are just four simple-seeming pieces to fit into each side of the tray, but they're much trickier to get your head around than you'd think, and there's only one solution per side! This award-winning puzzle design is available again for the first time in many years!

The Calibron 12-Block Puzzle was originally copyrighted in 1932 by the son of Thomas Edison; it has been unavailable for over half a century. Can you assemble the 12 blocks into a single, solid rectangle? Just how easy a puzzle do you think an Edison would design?

Of course, I still offer all of my earlier designs, too; it's a perfect way to satisfy (or frustrate) that puzzling person on your gift list. Just imagine the look on their face when they find one of these puzzles in their stocking!

Posted by Pavel at 11:06 PM | Permalink | Comments (0)

Even before I began designing my Anansi's Maze puzzle, I'd been thinking about how to create puzzles that intrinsically relied on the transparency of the pieces. My inspiration was a relatively unusual and little-known sub-genre of mechanical puzzles, sometimes called overlapping puzzles, in which the pieces have openings or transparent sections and your goal is to find a way to stack up those pieces and form a picture from the intersection of their transparent bits. The first puzzle I know of in this family was released way back in 1900, but there's been a steady trickle of examples ever since.

I got one such in the Puzzle Exchange at one of my first International Puzzle Parties. It consists of six octagonal pieces of transparent acetate, each laser-printed with a gray-scale image; if you stack up the pieces just right, the gray bits combine and darken and you end up with quite a nice picture of a dog, if I recall correctly. Mostly, I remember it being really difficult.

Still, the notion had stuck with me. I wanted to play in that design space, but I also wanted to make a puzzle that wasn't so tough to solve. I had the idea that I could make it easier by sharply reducing the number of layers, maybe using only two or three. To keep it from becoming trivial, I could break each layer into multiple pieces, so that you'd have to assemble the layers themselves before you could stack them up.

So far, so good, but then I got ambitious: what if you could assemble the layers in more than one way? What if you could form either of two different pictures from the same pieces, depending on which assembly you built? This whole story got me pretty excited: this could be a really cool puzzle! Now I just needed to actually design such a thing...

And there the idea sat, more-or-less unmoving, for almost two years.

The problem was, I had no idea how to go about creating this kind of a puzzle. Unlike many of my designs, I couldn't see any way to write software to help me search for a puzzle that would match my story; one of my key design tools had been stripped away from me!

I finally picked up the idea again late last winter, when I was trying to come up with a new mechanical puzzle for use in this summer's Microsoft Intern Puzzleday. There wasn't anything magical about the process, I just dug in, started drawing potential pictures, overlapping them, and looking for interesting area intersections. It was a very incremental, iterative design journey, one of the most difficult puzzle-design efforts I've been through. Even after I'd finished the artwork, what I'd thought of as the hard part of the process, the design went through five different prototype and test-solving iterations before I finally hit on the right combination of cleverness, accessibility, and clarity of solution.

In the end, ironically, the puzzle was completed too late to be used in Puzzleday, but I did use it as my Exchange at IPP 30 in Osaka later this past summer. I had barely enough copies made then to satisfy the Exchange rules, with just a few left over at the time for selling. By the time I finished with building those, I knew that I wanted to do yet one more, fairly minor design iteration before putting the puzzle up here on the website. What with one thing or another, it's taken me a while to do that iteration, but now it's done, and I'm quite happy with how the puzzle has turned out. I hope you'll enjoy it too!

Posted by Pavel at 10:42 PM | Permalink | Comments (0)

As I've described before, there's a marvelous biennial conference in honor of Martin Gardner called, appropriately enough, the Gathering for Gardner. It brings together three communities that Martin was active in, and in which Martin was very influential: mathematicians, puzzle people, and stage magicians.

No, really.

Each conference has a theme, and that theme is the sequence number of that conference. My first Gathering was the eighth one, so its theme was the number 8. (Did I mention the mathematician connection?) Anyway, everyone who comes to the conference is supposed to bring something for everybody else, all 300 or so of us, and ideally it will be something related to the theme number. I thought I was pretty clever when I came up with a very eight-related puzzle to give everyone.

My friend Bob Hearn, though, took literal-mindedness to a whole new level: he designed and gave out a puzzle that was entirely built out of the word "EIGHT". He found a clever style in which to draw the letters in "EIGHT" so that there are lots and lots of ways to neatly link those letters together, and then he picked a particularly cute couple of those ways and turned each one into a tray-packing puzzle.

The "Easy Eight" side of the tray appears perfectly straightforward, just a simple square. The problem is that it's kind of tricky to figure out how to get all five letters to lie flat in there at the same time: so many cute ways to fit the letters together, only one way to actually pack them into the tray.

Bob couldn't just leave it at that, though. No, it wasn't enough for him to create a really clever and elegant puzzle. He had to do it twice, with the same set of pieces. The (unique) solution to the "Hard Eight" side of the tray is equally clever, and equally elegant, and awfully tricky to find! It probably never occurred to you before, but an ellipse doesn't have any corners. None at all. There's no obvious way to start on this side, no clear surety that you're making any progress at all until, suddenly, there it is: the pieces are really, really close to fitting in. A little more tweaking, some tiny adjustments, and then you realize you're still not putting them in correctly!

Ahem. Sorry, got a little carried away there. Just a little puzzle-frustration flashback. I'm fine now.

As soon as I finally solved both of Bob's lovely Eights, I started talking with him about offering a version of his puzzle on this website. It's taken me a long time to pull it together (the tolerances for the "Hard Eight" side are pretty tight), but I've finally succeeded, and now I can make this wonderful creation available to you. This is a puzzle you'll enjoy solving yourself, and then really enjoy torturing your friends with. Really, what more could you ask?

Posted by Pavel at 10:03 PM | Permalink | Comments (0)

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!

Posted by Pavel at 09:39 PM | Permalink | Comments (0)

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.

Posted by Pavel at 05:25 PM | Permalink | Comments (0)

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:

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.

Posted by Pavel at 04:25 PM | Permalink | Comments (0)