Back in 2012 I was fortunate enough to attend IPP, and during the Puzzle Party day where you can buy and sell puzzles, I was able to purchase myself a copy of George Bell's exchange puzzle "Lomino Cube 4". George is a regular reader, and often comments on my posts, so I'm waiting with interest to see what he thinks of this review!
So what is a Lomino? Well the puzzle pieces used are all "L" shaped, and were named "Lominoes" by Alan Schoen, or so George tells me in the introduction to the puzzle. Lomino cube 4 is a set of 13 polycubes which have to be packed into various 2D and 3D shapes. A complete set of lominoes of order n consists of all lominoes that fit inside an n x n square. This puzzle consists of two complete sets of order n=4 plus one extra L tetromino (of volume 4). In the accompanying booklet, George sets out ten puzzling tasks which he lists in roughly increasing order of difficulty.
The image above shows the state the puzzle is deliver in, with the two complete sets packed into the "accordion" grid with 4 gaps remaining. As I'm sure you can guess already, one of the challenges will be to put that last Lomino into the accordion along with all the other pieces. But that's not the first challenge!
The puzzle is made from laser cut parts which are all a good size. Each cubie is 3/8" and the pieces are cut from clear acrylic. As you will see in the photos, the clear pieces make for some amazing finished objects, and I'm sure if I had more time, you could create some really nice effects with the right lighting. The tray itself is cut from three 1/8" thick sheets of acrylic, and are joined together to give the striking sandwich appearance with the solution shape showing through in bright orange, against the royal blue of the rest of the tray. Of course it didn't need to be 3 layers thick, but George added a second solution shape on the back of the tray, adding to the challenges. And that's not all, there's a third solution tray shape on the back of the booklet. There's a lot of puzzling in these ten challenges!
The first challenge is to create an 8x8 square, using all the pieces. Given that there are several tens of thousands of solutions (814,732 in all), I don't really have a problem showing just one of them here. I have no doubt that any puzzler with a little time can find a way to fit the pieces into an 8x8 square. From there, the next challenge is a little more difficult. Create a 4x4x4 Cube.
Now, I may have exaggerated. There's over 3 million ways (3,391,045 to be exact) to construct a 4x4x4 cube, so again it shouldn't be too much of a challenge. This time it's a 3D solution shape and given the reasonably small size of the pieces, and their slick finish, you may find yourself knocking the pieces over as you work toward a solution. That may just have been me and my fat fingers though.
Another of the challenges is to fit all the pieces into the "quilt block" shape in the reverse side of the tray. Again there are hundreds of solutions (406 in total) so giving away just one isn't that much of a help. You'll have no real problems in finding a solution yourself. There are a few other challenges involving packing the pieces in various ways, the last of which is to create a 3D shape which looks like the Dome on the Capitol Building. George doing his part to help make the puzzle themed to the IPP destination that year.
Once you've solved all of those, there's a set of 4 additional challenges to really test you. I'll not spoil them, but it's fair to say that they will make you think, and really add to the challenges. One of the more interesting from my perspective is to pack all the pieces into various solution shapes, where no two identical pieces have touching faces.
Overall, given that I have found a liking for packing puzzles, the Lomino Cube is a very approachable puzzle, with many solutions to each of the challenges (mostly) so that you don't feel frustrated by not being able to solve one, and can easily lose many hours to the puzzle. It's also well designed that all the pieces can be fairly readily self-contained, and that makes it a good puzzle for traveling. If you don't have a copy, head over to George's website, and see if he has a copy available, you'll not be disappointed.
As many of you know, I've owned and solved all of the Revomaze Series One puzzles released, including the Gold puzzle, which I'll write about soon. For a long time on the Revomaze Forums, a clear sleeve which would allow you to see the maze as you solved it has been talked about and many people have asked for one. Well having added the lathe to my list of tools, I thought I'd have a shot at making one.
Since getting the lathe, I've made a few pens, some bowls, all just learning how to use the tools, and get the shapes I want made. I mostly work with wood, as that's where my real love is, however I have played with a few acrylics as well. I find the acrylic to be a pain to work with, since it tends to create thin streamers of plastic which just wrap around whatever you're working on, and obscures your view of the work. Still, there's no way I could make a clear sleeve from wood.
It all starts with a block of clear acrylic. This piece is 2"x2"x8", which will be enough to make two sleeves. I got it from Tap Plastics here in the bay area. They'll custom cut sheets while you wait, and their prices are pretty good. I'm no expert with the plastics, but I can certainly recommend them.
First up, I need to take this perfectly clear block, and make a complete mess of it; otherwise known as turning it round. Doing that removes the beautiful clear finish, and turns the whole thing a rather cloudy opaque grey colour. When I'm working with Acrylics, I need to wear my respirator, as the smell created when working it tends to give me a headache. Not bad practice anyway, but something I have found I have to do. As it turns out, I'm also somewhat allergic to the material too. When I'd finished turning the block into a cylinder, and brushed all the tiny shavings off my arms, I found that I'd reacted rather badly to it. Time for a shower and some anti-histamine!
Having cleaned up, and put on long sleeves, I came back and shaped the outer surface of what would become the sleeve. Using the sleeve from my bronze maze as a template I matched the dimensions as closely as possible, including the ridges along the main body of the sleeve, and of course, making sure that the length was exact, since the intent is to make a fully functioning sleeve.
At this point, I've kept the sleeve attached to the main piece of perspex as I still need to drill out the central hole where the shaft will be. Before I go and drill that out though, I want to get the clear finish back so that I can see what I'm doing when drilling things.
After around half an hour of work, I end up with the finish above. This is wet sanded all the way up to 12000 grit to give a finish close to how the block arrived.
With that done, and the cylinder being transparent again it's time to change our the tail stock on the lathe for a 15/16" forstner bit to drill out the hole in the sleeve. Given the length of the hole I was drilling, the drill bit alone wasn't going to be long enough to make the cut. I had bought a bit extender so that I'd be able to drill the length I needed.
As you can see, with a sharp bit, the cut creates long streamers at the beginning of the cut, but before long, the heat almost melts the acrylic, and you have to be careful to eject the shavings before they solidify behind the head of the drill bit, and make it impossible to remove the drill bit.
Even though the drill leaves a rough surface on the inside of the sleeve, given the work sanding it earlier, it looks really good. Once the entire core is drilled out, it will be sanded up to 12000 grit the same as the outside, before being polished to a high shine.
Having completed the drilling of the core, I parted off the sleeve, and finished sanding the ends to get the same finish as the rest of the sleeve, things are just about ready. Some plastic polish is applied, and then a coat of Ren Wax to really finish the shine. As you can see, the inner core isn't perfect, but with more sanding I could get things back to a perfect finish. In fact I've gone back and made a second sleeve without the ridges which is far clearer than this sleeve.
So the real test is left. Can you see the core? Well the answer is a resounding yes. The core is easily visible in the sleeve, and everything fits perfectly. I'm pretty happy with the results.
Carrying on with my review of IPP31 puzzles, here's another of the puzzles that I picked up when I was at the recent Post IPP California Puzzle Party. Tromino Trails was Stan Isaacs exchange puzzle from IPP31, and given that Stan was the host of the Puzzle party, it would have been rude not to buy one of his puzzles.
Tromino trails is designed by Donald Knuth and made by Pavels Puzzles. You can read Pavel's description about the puzzle by following the link, and also purchase a copy for yourself if you'd like one. And I highly recommend you do!
This puzzle goes back to 2009, and IPP29 in San Francisco. There Donald Knuth gave a talk about varying puzzles he was working on and passed out a sheet with some puzzle problems that people could play with later. One of those problems was the Tromino Trails problem. I'll let you read about it on Pavel's site, as he was there and will explain it far better than I.
However I digress.The Tromino Trails puzzle is a physical version of Don's paper problem from IPP29. The puzzle consists of 24 L shaped trominoes with varying paths marked on them, a tray that can be configured to a number of different sizes and five challenges.
You start off with a 6x6 square, and 12 pieces, with the goal being to fit the pieces into the tray and form an unbroken loop with the trail marked on the pieces. There's a single unique solution to the problem. Given that the tiles are transparent, the trail is visible on both sides, and therefor can be flipped over and rotated as desired.
You then move a few bars around and get a larger 6x8 tray, add four marked pieces, and have the same goal of an unbroken loop. Again this problem has a unique solution.
Moving the tray around is easy as the spacers all have tabs on their ends that fit into notches in the tray and have a number of dots based on the challenge you're attempting. A great idea and really well thought out.
Next up a 6x9 tray created by moving more black frame pieces, and two new trominoes. Same goal, same unique solution ... are you seeing a pattern yet?
All five challenges, add progressively more pieces, and a bigger tray until you're using all 24 trominoes, all with unique solutions, and you have a beautiful, and elegant puzzle design. I think the nicest thing about this (given that we know I'm not good at tray packing puzzles) is that this one is really approachable. I've been able to solve all five problems, and none of them are too difficult. Yes they're a challenge, but not such that you get frustrated and want to throw the puzzle across the room.
There's no solutions provided, but if you are stuck, or just curious, then click the 6x6 solution link or the 6x8 solution link to see the solutions. After that you're on your own. After all, what's the point in my giving you the solution. This is actually a fun tray puzzle!
Eric Fuller recently offered a few new puzzles through Cubic Dissection and I picked up "Zauberflote" designed by Gregory Bendetti as well as "Stand Py Me" which I reviewed recently. Both puzzles sold out very quickly.
Zauberflote translates as "Magic Flute" and is an opera in two acts composed in 1791 by Wolfgang Amadeus Mozart. Gregory wanted to make a series of puzzles which had a link to the opera which he enjoys.
In a change from my usual style, I'm not showing the completed puzzle at the top of the post, but rather the pieces. I'll get to the reason why soon enough. Eric has created this 4 piece version of Zauberflote from acrylic and yellowheart, and describes it as a pocket puzzle, given that its full length is just 2.25". Gregory gave the four piece version the full name "Zauberflote - Königin der Nacht", and each of the puzzle in the series with a different number of pieces in the flute has a different sub-name. I really like the use of the acrylic here, as even when the puzzle is solved (as you'll see below) you can still see the internal burr of the wooden pieces, which is a nice touch. Eric made 45 copies of this puzzle, and they are all signed with Eric's usual squiggle.
I spent about 30 minutes working on this puzzle, and after a few false starts I found a way to get all the pieces in place and the flute shape (or possibly more of a set of pan pipes) is easy to see. When I was solving it, I started by putting the smallest piece in first, and I required a couple of rotations to get the pieces into their final location.
Feeling quite happy with myself I put the puzzle aside for a few days. When I came back to it, I opened the trusty Burr Tools and created a model of the puzzle there. Now I fully expected burr tools to be able to put the pieces in place, but I didn't expect it to be able to give me an assembly given that rotations were needed (when I solved it). To my surprise, Burr tools came back with 72 solutions and one assembly!
Burr tools notes a 14.4.2 assembly and shows that it is possible to solve the puzzle without using rotations as I had. If you look very closely at the two images, you'll see that the internal burrs are in different locations showing that clearly it's a different solution. Also Burr Tools puts the largest piece in first, although I believe it is possible to insert the pieces in any order.
So having used burr tools, I think there are more solutions than it shows, even without the rotations. I did talk with Gregory as to whether rotations were intended, and he admitted that he hadn't checked for rotations, but it wasn't cheating, since I still solved the puzzle without forcing the pieces, and had found a solution that he hadn't. The solution with rotations is much shorter at 184.108.40.206 (if my counting is correct).
Overall, this is a fun puzzle, which isn't too hard and is very nicely made by Eric.