Message #389

From: Remigiusz Durka <thesamer@interia.pl>
Subject: John Bailey explains N-teract 4
Date: Sat, 04 Aug 2007 14:55:32 +0200

I was asked by J.Bailey to post explanation of the puzzle which we discussed few weeks ago.

—– Original Message —–
From: John Bailey
To: Remigiusz Durka
Sent: Saturday, August 04, 2007 2:43 PM
Subject: Re: N-teract 4

Remigiusz Durka wrote:
Monday, July 09, 2007, 9:21:54 AM | Remigiusz Durka
Hi! Could someone tell me what is that? http://home.rochester.rr.com/jbxroads/4cube.html I’ve tried and tried to see/understand how "that" is related to 2^4

John Bailey, author of http://home.rochester.rr.com/jbxroads/4cube.html answers:
Saturday, August 4, 2007, 6:58 AM John Bailey

N-teract-4 maps topologically to a 2x2x2x2 cube–in other words, it is a 4 dimensional version of the 2x2x2 pocket cube. The mapping is incomplete.
First let me list the complete parts: 1) number of corners, 2) number of sides 3) number of cubes (3D) These are 16, 24, and 8 respectively, just as with a mathematical tesseract or a 2x2x2x2 pocket cube. On the web page, the 24 buttons correspond to the sides (or faces) of the hypercube. Clicking a button causes the corners of its associated face to move just as they would on a 2x2x2x2 cube. The buttons are positioned graphically in the arrangement so that there is somewhat of a mnemonic sense to their location relative to the corners they move. The BLRF naming convention (for Bottom, Left, Right, or Front) refer to which face of the cubelet is twisted.

The mapping is incomplete with respect to orientation of the corners. As the corners of N-teract-4 are moved, they do not change orientation. There is an illusion of rotation on the web page version–only because of the graphic design of each face. Look carefully when you press a button. The corners change location but keep their original orientation.

Lastly, only one direction of twist is provided. A backward twist requires the button to be clicked three times.

Two other buttons are provided to make the resulting puzzle somewhat more tractable. With its cumbersome buttons, a multi-twist macro would be somewhat tedious. By adding a single button (West L’U …) a single macro is provided which breaks the symmetry of the west face. This is enough to recover the home position of the game when it is used in combination with an appropriate sequence of face buttons.

The design of the web page, ie its layout, is the result of attempting (successfully, I think) to accomplish these operations within the limited confines of the scripting language, Javascript. Check out the page’s source code. It is included directly within the web page’s html and available using right click, select view source on your browser. Three functions use only 8, 7, and 5 lines respectively. An additional 16 lines are used to initialize the corner images. That is the whole of the script! The remainder of the intelligence supporting the script is in the specific arguments of the function "twist()" which are associated with each button. These specify the rearrangement of corners to respond when that button is clicked. The script is embedded in a public key signed message as window dressing.

The puzzle is relatively simple to solve. I am no cuber but I can find my way out of the scrambled position by observation and simple trial and error. For a while, I explained this by the speculation that as the dimensions of a cube increase, the number of paths to solution increase faster than the complexity. Thus there are more solution paths for a 4D cube than for a 3D. Thus far, no one has commented on this conjecture.

One last observation. As inspection of the source code of the script shows, the programming of higher dimension cubes would be simple. The function: onClick= "twist(2,7,8,3)" needs only to be provided one additional argument to make a 5D version. On the other hand, arranging the graphics for a 2x2x2x2x2 showing the 32 corners in a recognizable pattern seems rather challenging.

Please feel free to relay this response to your discussion group. I would be happy to explain any points further. It may well be that N-teract-4 fails reasonable criteria for rubikness, however within its limitations it stands on its own. It was named thus because someone (possible Mark Newbold) suggested that if I called it a Rubik anything I would be liable for a visit from the intellectual property police.

Depending on how this discussion goes, I might revive my interest in the 4D cube and install a randomization function for the scramble button. At the same time, I should update the dead links. Sorry about that. It was written a long time ago (1998, check the Public Key Signature)

John Bailey
http://home.rochester.rr.com/jbxroads

—– Original Message —–
From: Remigiusz Durka
To: John Bailey
Sent: Saturday, August 04, 2007 5:23 AM
Subject: Re: N-teract 4

Hello!

Thank you for response. I’m really looking forward to the discussion so you can send me any information and I will send it to the yahoo group.