# Message #660

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

Subject: Re: [MC4D] Greetings

Date: Sun, 05 Apr 2009 22:27:26 -0000

— In 4D_Cubing@yahoogroups.com, Roice Nelson <roice3@…> wrote:

> Coincidentally, this question of parities came up and led to lively

> discussion only a few months ago. With the paradoxical feeling of a

> Buddhist kôan, let me just say you’re both right. There was much more to

> talk about than one might have guessed, and I think we fleshed things out

> pretty well.

I have looked in the database to find the parity present on the 4^4, and found the case which you have found in your solves, with the 2C pieces. I didn’t really think about this possibility, as my way of dealing with the last few 2C pieces works differently from the first load and works around this, though I suppose it breifly crossed my mind. I leave all the 2C pieces with one colour (I chose blue as it happens) to the end of the step of matching up 2C pieces. I bring them to one hyperface then flip them all first so that the one colour faces inwards, then match like centres on a 4^3. If the number of 2C pieces isnt a multiple of 4, I simply flip an odd number of these with the alg I use which flips 8 2C pieces, and this leaves a multiple of 4.

Thanks for bringing this to my attention, the discussion before and the parity log file you submitted were very interesting.

Matthew