# Message #1665

From: Matthew <damienturtle@hotmail.co.uk>

Subject: Re: Goldilock’s function

Date: Sat, 07 May 2011 13:42:00 -0000

Hi David, good to see you back.

It’s an interesting formula you have there, and I would also like a bit of background on how you derived it. However, I may have spotted a little problem with it, and hopefully the feedback will help improve the formula, or prove to not be an issue. It was discussed that deeper cut puzzles would require less moves to scramble them, since twists affect more pieces, and will thus move pieces around the puzzle faster. However, the formula doesn’t quite bear this out for the various types of face-turning dodecahedra. I hope I haven’t made a numerical error here, if I have I apologise.

Megaminx: 105 twists

Pyraminx crystal: 81 twists

So far so good.

Starminx: 381 twists

This is far deeper cut than a megaminx, but apparently takes over 3 times as many moves to scramble? That result doesn’t seem correct.

Pentultimate: 130 twists

I hope I haven’t made a mistake, and made false accusations against your work. Perhaps there is a way to introduce another parameter, either for the number of pieces moved during a twist, or perhaps the ratio of pieces which are moved, to those which aren’t? Regardless, good work here :).

Matt