Numbers Game
234 Puzzle
234 Puzzle by Michail Toulouzas
Something wonderful arrived from Greece earlier this year, a gift from Mike Toulouzas, a talented and award winning designer and craftsman who makes some of the most beautiful puzzles in his spare time. Generous of spirit and in celebration of life, friendship and a common passion for being puzzled, Mike sent these gorgeous gifts out around the world as a holiday and end of year present to some very lucky people. There have been a few other notable mentions of this puzzle from other recipients as well, and it is my turn to raise a glass to the maker, too.
colorful puzzle candy
The puzzle comprises a set of six polyomino pieces with the interesting property that each piece is made with one additional block, starting from a two-block piece and going on up to a seven-block piece. The pieces start to become oddly shaped as they get larger. They are made of beautifully colorful exotic woods and come nestled inside an even more lovely little figured case with tapered legs and a wood hinged lid that opens and shuts with a satisfying click. The challenge is to remove all the pieces and reassemble them into a cube. Easy!
Not so easy! Mike sent a request along with the gift, asking recipients to time themselves and to do this three times spaced out with enough time to forget the solution between each attempt. Just that request alone was enough to give me palpitations, as I have experienced Mike’s deviously difficult puzzles in the past. His Flatliner puzzle is so named because it may send you into cardiac arrest from frustration. Mike is a funny guy too.
He shared some of the story behind his “234 Puzzle” with me. “The idea came to me in 2021. I wanted [to create] a cube from cubic bricks [by] adding a block [to each subsequent piece]. I definitely believed that similar cubes exist but i was hoping that the way I wanted to add the block didn’t. My wish was to create something simple to understand with mathematical basis (although i have no knowledge about these).”
Mike mentions that although there are likely similar cubes in the world made of graduated pieces, he had another special requirement for his set. He wanted to, somehow, use people’s innate intuition against them, by making the pieces tempting to pair in certain ways, which of course would be the wrong ways. “It seems that simplicity tricks people at first but to a point of no frustration. Just enough to be adorable.”
He has used this idea or objective before. “I do have in the past designed in such ways but with more pieces 7 and 8, such puzzles are the 7 Piece Nightmare which also has 2 big pieces and the Trigo Cube but the building block was from isosceles triangles.” I asked Mike how he comes up with these diabolic designs, which seem so innocent but are quite challenging, and how he designed the 234. “Pencil, millimetre paper and tons of mistakes. This is no exception, and made same way.”
The name derives from how each piece is one cube larger than the next. Perhaps it could be called the 234567 puzzle? But that, Mike points out, is unnecessary and inefficient. “The name comes obviously from the counting blocks added to create the cube but the beautiful thing about it, is that the 234 name is enough because you can have also the rest of the numbers from all combination of the 234 so 2+3=5, 2+4=6, 3+4=7.”
Mike relates that the final version seen here took a bit of evolution as well. His initial prototype “had the last two pieces reversed glued and this gave more than 5 solutions. I was not happy about it because every time the players were finding another solution from the one I had in mind. So I kept trying to minimize that, and finally made the result the 234 you see today.”
As for the timing aspect, I can tell you I am not proud but at least the only one watching me was the cat, and he couldn’t even do it one time. Mike’s “simple” cubic dissection puzzle is brilliant and a lot of fun. There are a few common configurations that are so compelling you find yourself building them over and over without meaning to, and of course the last piece won’t fit. But perhaps because there are only a few pieces, and you know that you will find the solution, eventually, the process and experience is truly enjoyable. My longest time was 58 minutes – and that was the second attempt! I admit I recalled the final two pieces after that and the third attempt took about two and a half minutes. I was still impressed that even knowing which four pieces to focus on to start out with took a few minutes.
Mike is doing a little experiment with people who are familiar with these types of puzzles, or who think they are, at least, compared to novices. “So far the longest [time] is 68 minutes and the fastest is almost 8 minutes ...any other 1 minute or 2 minutes is by remembering the solution. That is why my request is to solve it three times with a great gap in between these times.” He says it is too soon to tabulate any summary of comparison results just yet, but he does have at least one important conclusion. “I have learned that there are still very nice things to discover about simplicity.”
234
I liked Mike’s idea of creating a cube from individual pieces of increasing size so much, that I used it to create a cocktail for the toast. The challenge was to use volumes of ingredients in a 2:3:4 ratio. Cocktail ratios are like blueprints, and while not all combinations will work, many do and it can be fun to find new mixtures that taste great. Some classic ratios include the 2:1:1 or 2:1:.5 found in a whiskey sour, margarita or daiquiri, or the 1:1:1 Negroni. A favorite mathematical cocktail ratio of mine can be found in the “Fibonacci” cocktails invented by Paul MacDonald.
For the 234 cocktail I was inspired by a classic called the “Adonis”, which is a lovely cocktail featuring dry sherry and sweet vermouth. It was named for a Broadway burlesque show from 1884 (credited as the first ever Broadway musical) but we can appropriate it here as another example of a handsome Greek like this puzzle’s creator. Various ratios for the Adonis exist but a commonly used formula has the sherry at a 2:1 to the vermouth, and the drink often includes a dash of orange bitters. I tinkered with this formula and after a bit of experimentation with the third component settled on a small amount of amaro Cio Ciaro, which brings additional notes of herbs and bright bitter orange to the drink. It’s a combination that add up! Here’s to the complex beauty of keeping it simple. Cheers!
a number of fine selections
234
4 cl fino sherry
3 cl sweet vermouth
2 cl Cio Ciaro
Stir ingredients with ice and strain into a favorite glass. Orange peel twist garnish.
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