Message #3061

From: damienturtle@hotmail.co.uk
Subject: Re: Introduction (+ news of my own)
Date: Wed, 28 Jan 2015 12:22:10 -0800

Hi David,

It has been so long since I last posted here, I took 5 minutes to even find it again!

You mention trying to create a physical 3^4 puzzle, and I wish you good luck, I’m sure anyone posting here wants to see that achieved. I’ve thought about it a little before, but didn’t get far. This closest I know of is simply the skeleton of the tesseract, as seen here: The Happier Cube! (Hyper-Cube variation), https://www.youtube.com/watch?v=KFUQyZ-4HQg maybe it could be used as a base for a puzzle? Maybe you have something far more elaborate in mind, please let us know if you make any decent progress.

https://www.youtube.com/watch?v=KFUQyZ-4HQg

The Happier Cube! (Hyper-Cube variation) https://www.youtube.com/watch?v=KFUQyZ-4HQg http://www.24cell.net This is the much Hyped Happier Hyper Cube (can you say this ten times?), which can change its dazzling colors when going inside out. …

View on www.youtube.com https://www.youtube.com/watch?v=KFUQyZ-4HQg
Preview by Yahoo

.
As it happens, I was going to be posting here anyway. I have been asked by fellow speedcuber Simon Crawford to give a talk on some mathematics of the cube at Edinburgh University on 18th February as part of an "Innovative Learning Week" or something to that effect, having given a similar but shorter talk in the past. He recently started a postgraduate degree there in some aspect of pure mathematics, so his research is poorly understood my myself as my postgrad research is in applied mathematics at the University of Strathclyde (I’m looking at certain types of networks). There is also to be a speedcubing competition, originally planned for the following weekend but now postponed to 21-22 March.

What does that have to do with MC4D? Well, after going through the standard talk material of why there are 4.3 x 10^19 states on a 3^3, I wish to give a short mention of commutators, and finish by saying that the approaches used for analysing the number of states and simple commutators can be extended to apply to a wide variety of puzzles. I then plan to show off some of the crazier puzzles found around here to that effect, perhaps 3^4, 3^7, something from MagicTile, and finishing with the mind-bending MHT633, with a 3-cycle commutator having been applied to each of them.

I intend of course to give credit where it is due, depending on which puzzles I show off, but I thought I should also state my intentions here as way of asking permission and because some may be interested to know that I will be showing off these puzzles. I’ve yet to check if there is any explicit guidance on using images from the software involved, but I will check that too before I proceed.

If there is interest, I will report back here with any noteworthy remarks I might get from my terrified audience!

Matt

P.S. While I am unlikely to be doing any solved around here any time soon, I still fully intend to return one day and resolve some unfinished business I have with these puzzles :)