Mike is a Saviour - Presenting the Tetris Octagram

This last week has been a really busy one for me with late finishes and not much time for puzzling. On top of all that, it was time, yet again, for me to write the consultant anaesthetists' on call rotas for our hospital. This is 3 separate rotas utilising 27 people with all their standing requests, one off requests as well as annual leave. When I left work on Friday night, I took with me 18 sheets of A4 paper printed double sided with all the information as well as ensuring that the various emailed requests were forwarded to my home email. Writing the rota this time took me a whopping 7 hours in front of my 24" iMac and absolutely exhausted me - I was in no fit state to solve anything or plan a blog post afterwards. To top it off, today I am on call myself and could be called in at any moment - so for this reason I am eternally grateful to my Hawaiian correspondent, Mike Desilets, for sending me a review during the week and taking the pressure off me - he didn't even know that I would be in need. This means that, if I don't get called in, I can do some of the DIY that I have been putting off for weeks - "she who must be feared" has been threatening me with another Whack! Ouch! if I don't reseal her bathroom this weekend and fix the mortice lock on the door too! So without further ado, I hand you over to Mike:

Jonathan Berindei’s Tetris Octogram. Euro in the background for scale. Looks small doesn’t it?

Aloha Kākou readers,

When you hear that greeting, you can always expect more puzzle talk from the islands. I’ve been in a writing mood lately and I find that its best to indulge the urge before it passes. It’s impossibly hard to write when you are uninspired. Thankfully, I have been greatly inspired by a few new puzzles recently, one of which I’ll cover today. This post was also stimulated by a comment on my last post from Steve (aka Boxes and Booze), which reminded me that my esteemed editor and publisher Kevin (aka The Mad Puzzler (Ed - I'm Puzzlemad not a mad puzzler! or am I?)) does not generally collect certain puzzle types—boxes for example (Ed - just trying to save myself from complete financial ruin). I was happy to realize that my post filled a gap in the blog. Thinking about it a little more, I recalled that packing puzzles also constitute a distinct minority at Puzzlemad (Ed - I just can't seem to do them). There are packers on this blog, just not very many relative to the abundance that exist. Happily for the blog, I very recently played with a great 2D packing puzzle that I think is Puzzlemad material.

I give you—the “Tetris Octogram”—designed, made, and sold by Jonathan B from his workshop in northern California. This very attractive version of the classic octogram is an original design. I know this because Jonathan told me so, and also because I searched high and low for similar designs and found almost nothing. The Tetris Octogram is, of course, a polyomino packing puzzle, a class which has deep historical roots. Octograms are so named for the fact that the packing space measures 8 units on a side. Other than that, there don’t seem to be any strict rules. From a design standpoint, one simply selects a set of polyominos that are challenging to pack and aesthetically pleasing. Jonathan has selected a diverse set of 13 polyominos for his puzzle consisting of 1 heptomino, 1 hexomino, 7 pentominos, and 4 tetrominos.

Pentominos are traditionally the most popular pieces for this type of puzzle (and arguably the most popular of polyominos period), but I think adding the larger hepto and hexo pieces, as well as the unassuming tetros, was a good choice. I would go so far as to claim that this is a completely unique arrangement. Of course, with all the possible combinations of polyominos available there are surely many hundreds of unique sets to choose from. All I can say is that this particular set works, both aesthetically and from a puzzling perspective. Jonathan’s original inspiration was a children’s polyomino puzzle, from which he drew some of the pieces. He then selected the rest to complement these such that the final design was “equal and proportional”. Another influence was Tetris, hence the name of the puzzle. There are four tetris-derived pieces in the puzzle, also known as tetriminos to us GenXers (Ed - that would seem to include me).

Polyomino breakdown for the Tetris Octogram.

When I first considered buying the Tetris Octogram, I was attracted to the unique construction and materials but wasn’t terribly concerned about the puzzling aspect. Polyomino packing seems somewhat mundane compared to the many highly innovative and cutting edge puzzles that populate the blogs. However, I must say that this puzzle has really grown on me. It is not easy to solve, nor is it terribly hard to solve. But it is always fun to solve. And replay value is literally unlimited. There must be thousands of possible solutions (making solving highly manageable) but it is highly unlikely that you will take the time to memorize any one of them. So each play is basically a fresh start. In typical packing fashion, you’ll get within a hair's breadth of the solution and then have to backtrack and rearrange until you can create the space you need. It’s a very satisfying puzzle with a good balance of frustration and release.

My admittedly limited research produced only one other Octogram design available on the market. This is an all-wood Octogram of quite different design (meaning different choice of polyominos) made by the Kiwis at Puzzlingworld. Their version is composed almost exclusively of pentominos and one lonely tetromino. At least two separate programmers have analyzed the Puzzlingworld Octogram, coming up with 16,146 unique solutions (excluding equivalent orientations). This gives you some idea of the order of magnitude of the solving possibilities for the Tetris Octogram.

The Tetris Octogram has its roots in the octograms of the late nineteenth century, particularly the checkerboard  puzzles. The objective there was to fit a set of polyominos into an 8 x 8 unit square such that a regular checkerboard was created. The component squares of the polyominos alternate red and white. The earliest of these, dating to the 1880s, was the Sectional Checkerboard which included 15 polys: 9 pento (2 of which are duplicated), 2 tetro (both same), 3 trio (all same), and 1 domino. This was apparently a VERY popular and long-lived parlour (Ed - corrected to the correct spelling with a U in it!!) puzzle, spawning well over 300 designs (see Slocum and Haubrich’s Compendium of Checkerboard Puzzles, or better yet, just go here).

3/16th inch iron goodness.
Laser cutters are fine, but I want a plasma cutter!

As mentioned, the appearance and materials of the Tetris Octogram puzzle really pulled me in and ultimately made me hit the “buy” button. You can see from the pictures that this is a very substantial puzzle; the exact antithesis of the jewel case packer. The packing tray is a 9.5 x 9.5" slab of ¾" oak and the puzzle pieces are 3/16" thick iron. Jonathan cuts the pieces with a computer controlled plasma cutter (Ed - drool!). The polyomino designs are created on the computer and then fed to the cutter. Note that the polyominos are very nicely rounded, making them pleasant to handle and easy on the eye. They also have a nice fit in the tray—not too tight, not too loose. Overall, it’s an excellent piece of modern craftsmanship. The puzzle looks as good in person as it does on the web page, which is not always the case these days. Given its stout construction, this puzzle will also make a great multi-generational heirloom - I’m quite sure that it will outlive me. And unlike the more obscure puzzles I own (and cherish), I believe my non-puzzling descendants will appreciate it and keep passing it down. For myself, I intend to bring this puzzle back to the family lake house (a very modest one, don’t get the wrong idea) in Vermont and play with it before a crackling fireplace, warm cup of tea in hand. Thanks Jonathan.

Hrmmmm.........?

Only three Tetris Octograms have been made to date and I am the happy owner of number three. Jonathan is not a professional puzzle designer and he does make a lot of other stuff with his machines, so I asked him if this was just a one-shot lark or whether there are more in store. I was very happy to learn that he has plans for more designs, and in more sizes. I’ll definitely be keeping an eye on that. This was a great freshman effort and I’m excited to see what else he can come up with in this rather unusual medium.

You can find the Tetris Octogram at Jonathan’s Etsy store (unfortunately Jonathan has stopped producing puzzles. Price is $88 US (Ed - he doesn't seem to ship to the UK unfortunately) and he  makes them to order (pretty quickly in fact). This is not cheap, but you are getting a very high quality item of unique design. It is most definitely good value in my book. Jonathan spends upwards of three to four hours making each puzzle, plus material costs. Do the math. It’s a good deal. 


Ed - Wow!!! That looks absolutely stunning - whilst I am not a huge fan of packing puzzles because I struggle to do them and because there is just too much trial and error involved, this looks perfect. Hopefully someone will convince Jonathan to ship outside of the US so others can enjoy this great looking puzzle. I really will be interested to see what else he comes up with.
Thanks to Mike for letting me off the hook and for producing yet another stunning review - if you think you can also produce something equally informative then contact me on my Contact page.