Pavel's Puzzle Blog

I originally blogged about this puzzle a couple of years ago, shortly after I got my first copy of it, six years in the making. A few days after that, I got email from my friend George Miller, telling me that he'd laser-cut his own copy and liked it a lot. He showed that copy to long-time IPP attendee Stan Isaacs, who asked me for permission to use it in the IPP 26 Exchange, in Boston. At the time, I had a different puzzle in mind for my own exchange gift, so I agreed. Unfortunately, that other idea fell through (sometimes that happens with puzzle designs), so I ended up not exchanging that year. Instead, I was Stan's exchange assistant, which was fun in its own way.

The version that Stan exchanged was somewhat different from my original copy: he and George reshaped the pieces from rectangles to half circles, making the completed puzzle into a sphere instead of a cube; they called it the "Fan-Way Park Ball", following the Bostonian theme. They also used laser-cut maple instead of plastic and reduced the size to about 1-5/8 inches. It was cute in its own way, and I was happy to see the puzzle exchanged, but I still preferred the clear Lucite look of my original version; it looks a bit more stylish sitting on your desk.

I'm now happy to announce that I can offer copies of my version for sale here. The puzzle is shipped disassembled, flat, and putting it together provides a very satisfying but accessible solving experience.

Posted by Pavel at 02:56 PM | Permalink | Comments (3)

Flush with the successful design of the "Perkinson Guest Bathroom Tile" puzzle, the obvious next step was to consider dominoes instead of trominoes. This time, I allowed the pieces to be flipped over, and I also counted pieces whose two tiles had their tilted edges at right angles to each other. This leads to a complete set with 13 members, some of which are slightly strange looking, and one of which (with the two tilted edges joined together) is a quite boring perfect rectangle.

Leaving out the boring rectangle, we get twelve roughly one-by-two-unit dominoes; the obvious tray shape is a six-by-four-unit rectangle. Can the (nearly) complete set fill that tray? Sadly, my packing program said no, and this time it also didn't work to change the top and bottom edges into the angular "sine wave" pattern from the bathroom-tile puzzle. I had my local laser cutter, Joe Pelonio, make me up a set of the pieces anyway, so that I could play with them and try to get a feeling about why the rectangular tiling wouldn't work. The first thing I noticed when I got the pieces in my hands was that one of them looked a lot like the profile of one of the famous "moai" heads from Easter Island; thus the eventual name of the puzzle.

When I presented Easter Island Dominoes at the 2007 IPP Exchange in Australia, I told the following story:

It's not well known (especially to archaeologists), but many, many sets of these 12 pieces have been discovered in excavations on Easter Island. Never, though, have they come across a copy of that elusive 13th piece, the perfect rectangle. From this, we can infer that the ancient Easter Island culture, now long lost to us, did not approve of straight lines and perfect rectangles. Being a culturally sensitive fellow, I've created a tray that has one tilted tile edge exposed on each edge of the tray, thereby avoiding violating the islanders' taboos.

Your first challenge in solving this puzzle is simply to lay all twelve pieces flat in the tray; there are 250 ways to do that, and it's not very difficult if you just have a bit of patience. You'll find, though, that almost every such packing has at least one blemish (as least from the point of view of ancient Easter Island culture): there will either be (a) a straight-line crack all the way across or down the puzzle, or (b) a subset of the pieces that form a perfect rectangle or square, or (c) both!

There are just 83 ways to pack the pieces without a straight-line crack, and only six ways to do so without forming a perfect square or rectangle. Your real challenge is to find one of merely three solutions that have neither "blemish". That'll take you a little bit longer to achieve, I think.

Posted by Pavel at 07:53 PM | Permalink | Comments (0)

In the fall of 2004, I was playing around with a deceptively simple little tray puzzle designed by Stewart Coffin and called Four Sleazy Pieces. The eponymous pieces are polyominoes with between five and seven squares each, and the tray is a perfect square whose size is not an integral number of units; it's about 5.8 units on a side. I won't spoil Coffin's fine puzzle here, but suffice to say that, at the time, I hadn't solved it very recently so I'd temporarily forgotten just how "sleazy" the solution is.

While failing to solve it, I stumbled across an interesting property of such a puzzle, and I was excited to note that what I'd found was probably a good psychological "blind spot". These blind spots usually take the form of an assumption most people make that's so "obvious" that it's never questioned, even though it isn't in fact true. Armed with such a blind spot, you can often create a puzzle to exploit it, a puzzle whose solution violates that implicit assumption. That kind of a puzzle has a very pleasant "ah-ha" feeling to it; once you've solved it, you can't figure out how it could possibly have taken you so long.

My resulting puzzle, Sleazier, has that property, and I'm inordinately pleased with it: I think that it's probably the best puzzle I've yet designed. I presented it in the 2005 IPP Exchange, in Helsinki, and it's gotten great feedback in the years since then.

Like Coffin's puzzle, Sleazier has four polyomino pieces ranging from five to seven squares each, and a square tray of a suspiciously odd size; your goal is simply to fit all four pieces flat in the tray. I won't say why, here, but when you compare the "trick" of my puzzle to that of Coffin's, mine definitely deserves its name.

Posted by Pavel at 07:49 PM | Permalink | Comments (2)

In my very first IPP Exchange, in 2000, I presented a puzzle designed by Bill Darrah, called Raft 5. It consisted of 10 sticks, each with a dovetail notch cut across it and a matching dovetail tab glued on along it. There were five different positions on the stick where a notch or tab could be located, for a total of 10 different pieces, and the puzzle contained one of each. Somewhat surprisingly, it's actually possible to assemble these 10 pieces in a raft-like arrangement, with five sticks going one way laid across five going at a right angle.

Raft 5 is a good puzzle, and for the 2003 Exchange in Chicago, I decided to take inspiration from it. The raft is essentially two dimensional, and I wanted to somehow extend the idea into 3-D. To keep the number of possible pieces down, I made my sticks shorter, with only three positions where a notch or tab could be placed, but I also made the sticks square in cross-section (as opposed to rectangular, as in the raft). This allowed tabs and notches to appear on different sides of the stick, even at right angles to one another.

If you leave out the cases where a notch and tab appear in the same position along the stick (unless they're on opposite sides of the stick), then you get a total of 14 possible pieces. That seemed like too many for a good puzzle, so I picked just half of them; I was perversely tickled by the idea of using seven pieces in an interlocking puzzle, instead of the traditional six. Of course, seven pieces can't make a very symmetric shape, but I made a virtue of that, and designed the puzzle so that the final shape isn't particularly important. Instead, the goal is simply to arrange the pieces so that every piece's tab is inserted into some other piece's notch; that forms the pieces into a kind of folded-up loop, each inserted into the next, like a snake eating its own tail.

There are four solutions to the puzzle, two of which have the fun property that the resulting assembly will balance nicely on the end of one of the sticks. Those two solutions look a bit like a figure standing on one foot, which I like quite a lot; at some point, I want to make a very large set of the pieces to use as a bit of artwork for our yard.

Posted by Pavel at 07:40 PM | Permalink | Comments (2)

For the 2002 puzzle party in Antwerp, I wanted to design something that would lead people to explore the strange world of Penrose's non-periodic kite-and-dart tiles. Some years earlier, someone else had already exchanged a Penrose-based puzzle; that one was just a set of kites and darts that had been distorted a bit to resemble two kinds of birds (and to enforce the normal edge-matching rules). The goal had been simply to fit them together to make the classic regular decagon that crops up every you look in any tiling.

For my own puzzle, I wanted to challenge you to do more than simply learn how to tile the pieces; I wanted it to be a real puzzle. I played around with a Penrose tiling applet for a while and came up with an outline that looked, to me anyway, a lot like the head of a man wearing a turban. That shape required 76 tiles to make, so I broke it up into a set of 16 multi-tile pieces, each containing between 3 and 5 tiles. I then laser cut and etched those pieces with Conway's beautiful curves that show where the legal edge matches are. The resulting puzzle has a unique solution and is fairly difficult.

To make it a bit easier, I added a little removable panel that reveals where some of the tile boundaries are (and that shows why I thought the shape looked like a Grand Vizier). I also included in the package a "little bit bigger hint" that shows where all of the tile boundaries are (but not the piece boundaries, of course).

Finally, I discovered that a subset of pieces I'd chosen could be assembled to form that same classic decagon I mentioned above, so I made the puzzle tray two sided, with the outline of the Grand Vizier on the front and the outline of the decagon on the back. Oddly enough, even though I don't tell you which subset of the pieces you have to use in filling the decagon tray, that side is definitely easier than the front.

Posted by Pavel at 12:40 AM | Permalink | Comments (0)

In 2001, the 21st annual International Puzzle Party was held in Tokyo, and I decided to honor the hosts with a puzzle based on the simple, elegant design of the Japanese flag, also known as Hinomaru (literally, "the circle of the sun"). To start, I drew the flag's design on a 6-by-4 rectangle and then broke it up into twelve 1-by-2 dominoes. Then, to make things tricky, I also colored the backs of all of the dominoes in ways that make them look like potential fronts. Thus, all of the dominoes are double-sided, and it's not at all obvious which side is the front! Add to this the high degree of symmetry in the flag design, which makes the piece placements even more ambiguous, and you have a very difficult puzzle.

(At the 2007 IPP in Australia, six years later, someone came up to me during the Exchange and said, "I spent a long, long time solving that flag puzzle of yours." He then handed me his Exchange puzzle. "This," he said, "is my revenge!" Needless to say, I haven't solved his puzzle yet...)

The Hinomaru puzzle has a unique solution (up to swapping pieces with the same face-up design), and that solution leaves only the front face looking like the flag; the backs of the pieces look entirely random when solved (no helpful hints there!).

I also have an all-paper version of the puzzle, consisting just of the 12 double-sided cards that are sandwiched inside clear acrylic in the version above. This version doesn't come with a tray, just the cards wrapped up in a simple origami envelope.

Posted by Pavel at 11:20 PM | Permalink | Comments (0)

When I was invited to my first International Puzzle Party in 1999, in London, I learned that I would not be allowed to participate in that year's Puzzle Exchange event. There's a very good rule that you need to have attended IPP once before you do the Exchange, to give you a chance to soak up a bit of the party's culture and quality expectations. I decided, though, that I would produce some kind of puzzle anyway, so that I could try to trade it informally for Exchange puzzles (and others).

The only problem was that I had never designed a puzzle before! I mentioned this issue to my friend Barry Hayes and his response was both surprising and surprisingly helpful: "There are puzzles all around us! Almost everything you see is a puzzle; the only tricky part is to recognize how."

As it happened, I was in the local home center the next weekend, buying parts for our garden sprinkler system. Surrounded by all these very uniform pipes and fittings, Barry's words came back to me and I decided that there must be lots of puzzles hidden in these bins. The first thing that came to mind, of course, was a puzzle involving water moving through the pipes, but it didn't take me long to reject that idea in favor of something, anything, less complicated, less "analog". But what else would neatly fill a pipe? Well, anything round would, like ball bearings and dowels...

The result, Pavel's Pipe Dream, is shown at right. There are five dowels, one starting inside each pipe, with notches on the dowels intersecting (and therefore interacting) inside each T fitting. The ball bearing starts just inside the (sealed) endcap in the lower left corner. To solve the puzzle, you must manipulate the dowels through the little windows in the pipes to eventually free the ball. I brought more than 50 copies of the puzzle to London, and succeeded in trading all of them (and the promise of another dozen or so more) to various of the attendees. I came back home after the party drunk with the fact that I'd added something like 65 new puzzles to my collection!

I don't have any more assembled copies of this puzzle left, but I've got lots of copies of the various bits and pieces lying around in the shop. It's not my favorite of my designs, but perhaps if there's sufficient demand I'll produce one more run of them for sale. Leave a comment if you might be interested.

Posted by Pavel at 01:24 AM | Permalink | Comments (0)

Last Saturday, we held one of the three central events of the annual International Puzzle Party here in Helsinki, the Edward Hordern Puzzle Exchange. This is, in many ways, the most highly anticipated event of the party, with most participants beginning to prepare for it starting back in December, if not earlier. This year, we had 91 people taking part in the Exchange, out of about 170 puzzlers attending the party overall.

The Exchange was scheduled to begin at 10am, and we got access to the hall, to prepare, starting at 9:30. Tables had been laid out in long lines across the room, one table and two chairs per exchanger (one chair for each puzzle's presenter, and one for their assistant, if any). Every table had an exchanger's nametag on it, and there was a schematic map at the entrance, to make it easier to find your station. On the stage at the front of the hall, there was another, shorter, line of empty tables, intended to hold samples of all of the exchange puzzles.

At my table, my assistant Michael Powell and I got to work unpacking the big box I'd brought in containing the puzzles I'd had made back home and then shipped ahead of me to Helsinki. We needed to work somewhat quickly, because I'd discovered the previous day that, during shipping, the sharp laser-cut edges of the puzzle trays had rubbed against one another, slicing many of their zip-loc bags into ribbons. We had to check every single bag and, in half or more of the cases, remove the puzzle and repack it into a new bag, purchased the previous day, with some effort, at a Finnish supermarket. (Do you know the Finnish word for "zip-loc"? Me neither.)

By 9:55 or so, we were ready, with one copy of my puzzle tagged and arranged on the samples table, and the other 91 (including one as a thank-you gift for Michael) stacked neatly in front of us on my table. Michael had our exchange checklist ready; all that remained was to wait for the signal to begin.

The Exchange is a heavily tradition-laden event that grew out of an ad-hoc practice at the earliest puzzle parties. Several of those early invitees brought little puzzle gifts for everyone else and handed them out. As the party grew, over the years, the Exchange was formalized and the key rules were set down. First, not every attendee at the party need take part in the Exchange; it's strictly voluntary, and only allowed for people who've been to at least one party previously. Second, every participant must bring many copies of the same puzzle, one for each other participant and one for the samples table; many people bring more, to offer for sale or trade at the official "Puzzle Party" the next day. Third, all Exchange puzzles must be original, never available before the day of the Exchange. Fourth, and most ambiguously, these must be high quality mechanical puzzles; paper-and-pencil puzzles, like crosswords, and jigsaw puzzles are not included. (The term "high quality" is intended to refer to the puzzle-solving experience, not necessarily to the materials or craftsmanship; in particular, "high quality" does not necessarily imply "high cost".)

At about 10:02am, this year's IPP host Tomas Lindén stepped up to the microphone and gave the signal: the 2005 Exchange was under way.

Over the course of the next five hours, Michael and I walked around the hall, meeting each of the other 90 exchangers, chatting a little bit, describing our puzzles to each other, and finally exchanging them. From time to time, Michael would carry the puzzles we'd received back to my own table and pick up another armload of my puzzles to give away. Since my table this year was off in a back corner of the room, we had a lot more success finding new exchangers by walking around the room ourselves. We tried a few times going back to my table and waiting for others to come to us, but with only marginal results.

By the end of the five hours, we'd checked off everyone on our list and Michael had packed up all of my swag in the boxes I'd brought. Another Exchange had come to an end.

I haven't had a chance yet to really take stock of the puzzles I received this year. There's always a few disappointing ones, and usually some pretty special ones, and I don't expect this year to be any different. I've already solved a few of them (an amusingly misleading tray-packing puzzle, a simple "Finnish thematic" tray puzzle, a level 7-3 three-piece burr, and a 39-move sliding block puzzle), and I've brought a few more with us on our trip to Norway, but the big review will have to wait until we and the boxes I shipped both arrive back home in the States.

What a cool thing to look forward to!

Posted by Pavel at 07:01 AM | Permalink | Comments (0)

I'm writing this from my hotel room in Helsinki, at about 5:00am local time. Kathleen and I arrived yesterday afternoon and, of course, the ten-hour jet lag is causing a little sleep-cycle disruption.

We're here for the 25th annual International Puzzle Party (IPP), an invitational gathering of serious collectors of mechanical puzzles. The definition of "serious" is pretty vague, but is intended to exclude the merely curious. (Though, as anyone here would admit, there are a number of pretty curious people here nonetheless.) To give you a sense of how serious "serious" can be, though, my collection of 600-700 puzzles is well down at the low end of the size distribution. There are many people here with several thousand puzzles, and a few amazing collections of 25,000 or 30,000 puzzles or more, some dating as far back as the 13th century. Believe me, Kathleen's getting off easy in the "whacko spouse" department (as least as regards collections).

The party location rotates every three years among Europe, the United States, and Asia. There will probably be around 200 collectors here, many with their families, from 25-30 countries all over the world.

The party doesn't actually start for a few more days yet, but we decided to come early to give ourselves extra time to explore the area and to get over our jet lag. To our inexplicable surprise, several other folks had the same idea, so the puzzle conversations have already started echoing around the lobby here.

I hope to be posting pretty actively for the next while, so keep checking back for more on Helsinki, puzzles, and Norwegian coastal cruises!

Posted by Pavel at 06:48 PM | Permalink | Comments (0)