# Message #2855

From: Roice Nelson <roice3@gmail.com>

Subject: Re: [MC4D] RE: New 4D solver :)

Date: Mon, 16 Dec 2013 11:16:11 -0600

Awesome! These new sequences from you and Michael come as a bit of a

surprise to me since MC4D has been around so long. It kind of makes me

wonder if some new "shortests" categories in the Hall of Fame would be

justified.

I also wonder if there might be a way to mathematically prove what the

shortest possible 3-cycle corner sequence can be (which doesn’t alter other

pieces). Given how difficult the 3x3x3 God’s Number problem turned out to

be, there might not be, but perhaps the extra constraints of the question

could make it tractable. And maybe there is a pattern: 8 moves in 3D, 12

moves in 4D, ?? moves in 5D, … Corner pieces always touch half the puzzle

faces, and perhaps the logic of an argument could start there.

Roice

On Sun, Dec 15, 2013 at 2:49 PM, <eero.neijonen@jyu.fi> wrote:

>

>

> Hello all,

>

>

> This is my first post here and as for the time being I’ve been happy to

> only read the digests of some of the conversations here. Then inspired by

> your info about the shortest algorithms I started to find out good ones

> again and found actually a 12 move 4-color piece 3-cycle. Then I thought it

> would be of interest to share it with you.

>

>

> So here is the algorithm in log file notation:

>

> 48,1,1 101,-1,1 185,1,1 101,1,1 48,-1,1 129,-1,1 48,1,1 101,-1,1 185,-1,1

> 101,1,1

>

> 48,-1,1 129,1,1

>

>

> My main idea was to look for a way to replace one 4-color piece in one

> side with 5 moves and then commute this algorithm with moving this side.

> The solution finally came by a bit of accident but anyway here it is.

>

>

> –Eero Neijonen

>

>

>

>

>

>