Message #3640

From: damienturtle@hotmail.co.uk
Subject: Re: Physical 4D puzzle achieved
Date: Fri, 10 Feb 2017 23:52:35 +0000

Melinda,

It seems that the choice of magnet arrangement isn’t correct then. Fortunately, I think that’s solvable. I now wish I’d fully understood this approach when you first discussed it, it took this prototype and some careful thinking before I finally clicked.

First of all, I think that taking a 2x2x1 block from one end and putting at the other end is a valid maneuver, a 4D rotation which will allow blue/red pieces to mix with other colours and to fully scramble the 2^4.

Then, how should the magnets be configured? Well, I see two possible solutions.

1) We need to be able to pick out any piece and put it back in any of the 12 orientations of 2^4 corners (which are the rotational symmetries of the tetrahedron) and be able to attach it back to the puzzle, which tells us the symmetry of any valid static arrangement of magnets. I skeched a solution quickly and uploaded it to the group (it’s in the group files in my folder since I’ve no idea how to attach images to a post): shown are 3 sides of one piece and 12 magnets embedded in those faces, with the colour of the dot indicating the orientation of the magnet. As a quick desciption, there are 4 magnets on each face in a ‘+’ pattern, with orientation of the magnets alternating as you go round the face. This is done such that if the cube is rotated about a corner the configuration looks the same. I believe this will result in a fully-functioning puzzle, but it takes 384 magnets!

2) It might be possible to have a spherical magnet in a cavity in the center of each of the 6 faces of each piece. When two faces are brought close to each other, the magnets should be able to realign so that they attract. This only takes 96 magnets, but I’m less convinced it will work well and robustly than a static configuration of magnets.

If I’ve made some mistake or someone has a better idea, I’d be interested in seeing it. Either way, I hope a physical 2^4 is available to buy some day, it would be so much fun to play with and show off!

Matt