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November 25, 2012

Holiday Discount Puzzle 2012

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!

Custom-Designed Jigsaw Puzzles

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!

November 23, 2012

Dali Bottles

Something very odd happened to this bottle...

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.

Hmm. The issue seems to be more widespread...

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.)

Wow. An even dozen bottles have been affected.

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!

Wait. They seem to be getting together...

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.

This is definitely stacking up to something very odd...

Several 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.

Well, that explains why the bottles looked like that...

It took us a while to refine our ideas and techniques, but we finally got something worth offering to you, the puzzle-buying public: we call it Dali Bottles. Each sculpture is made from about a dozen real beer bottles, plucked from certain doom in the recycling bin. We first melt each bottle separately in the kiln overnight, flattening it like all of the air has gone out of it. Then we stack all of the bottles up in a random, circular or square arrangement and run 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.

There is no airspace between those bottles!

As I said above, it's been several years since Sarah and I started this project and, in the meantime, Sarah has retired from teaching and moved onto a sailboat in the Caribbean. No, really! There's no room on the boat for her kiln, so she kindly sold it to me, and now it lives in my garage. However, I haven't yet put in the dedicated electrical circuit necessary to run it, nor gotten up to speed on making Dali Bottles myself.

The upshot is that, for now, we only have available those sculptures / puzzles that Sarah made before she retired. Take a look at photos of all of the sets we have on hand and then select the one you'd like from the menu below.

November 20, 2012

Trail and Error

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?

November 19, 2012

The Bricklayer's Challenge

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.

The first thing I wanted to change was to make it a little bit smaller: I remember Barry noting ruefully that the wooden one wouldn't even fit in his suitcase! Since I was making mine out of acrylic, I could also spice it up with some vibrant colors and translucent pieces. Although the mathematical idea behind the puzzle can work for any even number of pieces per row (and there's another puzzle for you: why is that the case?), after some consideration I decided to go with the same row size as in the original. It's a nice balance between complex enough to be non-trivial and simple enough not to get tedious.

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...

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