Gregory Benedetti on Coordinated Motion and the Beauty of Solving

photo_1The use of coordinated motion as a method for disassembling and reassembling a puzzle is something Gregory Benedetti has returned to over the years in a variety of shapes and levels of difficulty. In Little Slide Plank he has distilled this movement into its purest form: an unassuming 2x2x2 cube comprised of three pieces that come apart with a single move.

At first glance Little Slide Plank appears to be similar to Greg’s earlier Two Pi but differs in one important way. When opening the puzzle the sharp angles on all the pieces are immediately apparent, which as Greg explains below is due to his use of “planks” between the eight cubes of the finished puzzle that allowed him to fill the holes with half-cubes all cut along the diagonal. This lends a severity both to the look of the pieces as well as the opening motion.

This is a great puzzle for non-puzzlers to play with. It’s not intimidating, requires no explanation, and due to there being only so many ways that a three-piece cube can be pulled apart, they’ll have the pleasure of solving the puzzle and witnessing its strange opening movement.

The "planks", made from dark hardwood, can be seen between the ash tree cubes. (Photo courtesy Bernhard Schweitzer)

The “planks”, made from dark hardwood, can be seen between the ash tree cubes. (Photo courtesy Bernhard Schweitzer)

Coordinated motion is a particularly graceful subset of take-apart puzzles. The pieces lock each other into place unless they are moved in opposing directions at precisely the same time and at precisely the right angle. The opening movement of coordinated motion puzzles has been compared to the petals of a blossoming flower. To that description I’d like to add a flower that can blossom over and over. In fact, I still find myself picking up and playing with the puzzle when I walk past it just to watch it expand outwards and open. And this particular aspect can be found in coordinated motion puzzles regardless of the number of coordinate movements required or the number of pieces involved.

In October-November 2013 I spoke with Greg via email about Little Slide Plank and his love of coordinated motion puzzles.

Saul Symonds: You use coordinated motion in a lot of your puzzles. What do you like about this particular assembly/disassembly method?

Gregory Benedetti: I love the aspect of the transmission of the movement. This kind of puzzle reminds me of mechanisms which use gears. You move one thing and other things move with it, really funny and fascinating. Especially the fact that this mechanism is just a dissection.

SS: How did you first come across the idea of using coordinated motion?

GB: I saw some of Vinco’s designs on Guy Brette’s blog. I hadn’t seen this kind of puzzle before and I was fascinated. So I tried to design my own coordinated motion puzzle. I became a big fan of Vinco’s work. I have nearly all his CM designs. For around two years I have carefully studied all his designs, so that I have in mind all the classic ways to make a three-, four-, six-, and 12-piece CM.

SS: What is the process you used for designing Little Slide Plank and other more complicated coordinated motion puzzles? Is a computer used in any of this?

GB: For Two Pi (my first CM) and some others puzzles, I designed the main part of the mechanism in my head. The computer process helped me to see where the holes are and fill them, to give one example. Because Little Slide Plank is the same mechanism, I used the same process.

For more complex mechanisms, I use a computer at the beginning of the process, but I already have in mind the main part of the mechanism. (Most of the time, it’s the beginning of the CM, the number of pieces involved.) The software helps me to see the collision during the CM, and to complete the holes if possible. After that, I use Burr Tools to determinate all the other assemblies. I analyse all these assemblies to find out if they can be constructed or not. Each time, I use Burr Tools to share the puzzle with the community and craftsmen.Little Slide Plank (1)

SS: How much testing do you do with these puzzles? Have you made other coordinated motion puzzles that you discarded for one reason or another, for example, because you didn’t like the opening/closing motion?

Little Slide Plank (2)

The holes can be seen in an earlier version of the puzzle, which was made from three identical pieces. (Images courtesy Gregory Benedetti)

GB: I make a prototype in wood or I order one from Shapeways. Sometimes, I only virtually test it. If it’s not a classic design I give the puzzle to some of my close friends.

Sometimes, I had in mind an impossible mechanism and I realise it is impossible only after using the software, so I don’t finish the design. It’s my way to discard a puzzle. If the mechanism is functional I often share the drawings on Ishino’s website, even if the puzzle has inconveniences like requiring a high-level of dexterity.

SSLittle Slide Plank is a cube with only three pieces, but other coordinated motion puzzles you have designed use more pieces and have more complicated shapes. How do you decide the final shape the puzzle will have and what number of pieces to use?

GB: Sometimes I think about a mechanism, it’s difficult to explain, but I see a CM in my head. That is why it’s impossible sometimes. I can do this only with CM. I think it would be impossible for me to do it for high-level puzzles. So, I see a number of pieces which are moving together, sometimes I see the departure shape, but it’s often vague, and the final shape is revealed when I draw it on a piece of paper or when I begin to model it with CAD software. Easy Cage 1 is a good example of this.

Sometimes this method gives a shape that is so close to a cube that I decide to complete it. Little Slide Plank is a good example of this. For my polyhedral dissections, I tried to transfer this cubic method, so the shapes were a surprise.

Sometimes my departure point is the shape, it’s nearly always burr shapes and this has two opposite impacts on the number of pieces. The classic impact: a six piece burr with six pieces. The devious impact: it seems to be a six piece burr but there are not six pieces (for example Easy Base 4) or they are strangely distributed keeping the external appearance (for example CCBB).

SS: Little Slide Plank is an easy puzzle to solve but has a beautiful opening motion that kept me playing with it again and again. What importance do you place on the difficultly of a puzzle? And what importance do you place on the beauty of its solution?

GB: At this point I must be more precise. There are two kinds of puzzles which use coordinated motion:

  1. Explosion – one motion. Most of the CM puzzles fall in this category. Little Slide Plank is one of them.
  2. Puzzles using one or more coordinated motions or using coordinated motion like a step in the mechanism. They are rarer. I designed some like that, but the two references for me are Andreas Röver (father of Burr Tools) and Junichi Yananose (Tornado burr, Kamikaze burr).

Nearly all “simple” explosions are easy. And they all have a beauty during the solving process. Most of the time these puzzles are more fascinating objects than puzzling objects. If I design an explosion the difficulty is not really important. For this kind of puzzle, the biggest difficulty is to know where the pieces are in the final shape, this “puzzling” part of the solving process can be increased with color constraints like when Flattrick becomes Tri-Cycle.

A prototype of Little Slide Plank (Image courtesy Gregory Benedetti)

A prototype of Little Slide Plank (Photo courtesy Gregory Benedetti)

SS: You mentioned that your puzzle Two Pi has basically the same mechanism as Little Slide Plank. In fact, when I first saw the pieces online I thought it was the same puzzle. What was the reason for returning to this idea a second time? Do you think Little Slide Plank improved upon Two Pi?

GB: Little Slide Plank is a collateral design. I had in mind a mechanism using “planks” and more than one motion. I’m still working on this idea but when I modeled it I saw a nice possibility with a 2x2x2 cube.

So this is the same mechanical dissection, but the “planks” permit the functional surfaces to be linked more strongly. Another thing is that the “planks” allow the spaces be filled with a “half-cube”. It’s more confusing because there are only “half-cubes” and planks in the dissection, and you can eventually have a doubt between a filling part of the puzzle and a functional surface. So yes, Little Slide Plank is an improved version of Two Pi, but still a simple explosion.


Little Slide Plank
was produced in the New Pelikan Workhop in the Czech Republic and purchased from Bernhard Schweitzer at Puzzlewood

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2 Responses to Gregory Benedetti on Coordinated Motion and the Beauty of Solving

  1. Very nice interview…well done! John 🙂

  2. Pingback: Six Piece Cube & Little Slide Plank by Gregory Benedetti « Neil's Puzzle Building Blog

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