Rotating Beads Puzzle w/ Magnets

This bead puzzle is akin to the Rubik’s Cube and the vintage 1980s Hungarian Tower of Babel puzzle. You have to rotate the puzzle and move balls from one side to the other to solve it.

The idea was done many times before. It is a variation of a beads-permutation game that was sold in the late 1970s. It was initially made of wood. The Tower of Babel was made of plastic.

– https://www.aliexpress.us/item/2251832818790214.html (8-8-8-7 configuration)

– https://www.jaapsch.net/puzzles/ivory.htm (6-6-6-6-6 configuration)

The latter still exists as a wooden puzzle:

– https://www.winsharepg.com/spin_to_win (4-4-4-4 configuration)

– https://www.ebay.com/itm/234844467868 (6-6-6-6 configuration)

and as a 3D printable model:

– https://cults3d.com/en/3d-model/game/rotary-ball-puzzle(6-6-6-6-6-6 configuration)

It was revived 8 years ago by Cemal Cetinkaya for 3D printers:

https://www.myminifactory.com/object/3d-print-3d-puzzle-5117 (10-10-10-9 configuration)

The idea was picked up by Devin Montes 5 years later, who made several variations (in the shape of https://creazilla.com/nodes/73974-hexasphericon-with-captive-bead-track-3d-model):

– https://www.myminifactory.com/object/3d-print-astrolabicon-pro-114579 (6-12-5 configuration)

– https://www.myminifactory.com/object/3d-print-kwob-puzzle-rounded-114593 (6-5 configuration)

– https://www.myminifactory.com/object/3d-print-the-chain-twisting-marble-puzzle-118794 (15-14 configuration)

See also, this one:

https://www.printables.com/model/28299-astrolabicon-puzzle

While the idea was used many times before, this present design is fully mine. This is a 12-17-12 configuration.

I was frustrated by the feel of the ones I had seen before. The grooves weren’t the right size.

Honestly, mine is still not perfect so I am enclosing the Fusion 360 file so that people can modify it if they want. I am hoping that many people will remix the 3D files. I am also hoping someone will replace the middle piece with a cross: I haven’t had time to do it but it would be a cool project.

Which brings me to the beads. Supposedly, these beads are 14mm in diameter. However, the ones sold online are not. They are 13.6 or 13.7 mm in diameter. This means that unless you change the size of the channels of the puzzle, the beads will be all over the place. The puzzle will not “feel right”. It was a lot of trial and error before I got a “good” model. (I am putting a link to the bead in the comments.)

As I said, all these puzzles are perfectly identical to one another once we account for the difference in the number of beads and grooves. In fact, they are part of a family of mathematical problems in group theory called “permutation puzzles”. (The Rubik’s Cube is one of these problems. These beads problems are another one.)

http://www.sfu.ca/~jtmulhol/math302/notes/permutation-puzzles-book.pdf

Like for the Rubik’s Cube, there is an inefficient brute force way to solve the problem and an optimal minimal-number-of-moves way to do so. Unfortunately, while my first PhD was in mathematics, I studied set-valued analysis so I do not know what is the guaranteed minimal number of steps to restore order to the puzzle from any random position.

B.O.M

41 beads - ~13.7 mm diameter

24 magnets - 6mm dia x 3mm high

Printing

No supports. I printed the body in PLA and the plug in Prusament PETG orange.

I'll add a link to the beads I bought in the comments.