Message #1661

From: Melinda Green <>
Subject: Re: [MC4D] Re: Hi everyone, I’m back!
Date: Wed, 04 May 2011 12:47:56 -0700

Hello Nan,

Thank you for the link to the speedsolving scrambling rules. I guess
it’s not much help though it’s good to see how others have approached
this problem.

I understand what you are saying about scrambling for humans.
Specifically, after 10 twists or so, no human will save any time by
trying to carefully back out the scrambling moves, meaning that they
will have to perform a "full" solution. It is good to note that it may
be rather easy to back out 10 or even 20 random twists on the 120 Cell
because faces are very sparsely interconnected. I’m going to go out on a
limb here and say that I disagree that 1000 twists on this puzzle is as
good as 4000. Given the low odds of any given piece on this puzzle
finding itself on its opposite face, I would expect the length of human
solutions on 1000 twist scrambles to be consistently shorter than for
4000 twist scrambles.

As I was composing the above, I just thought of a potentially good way
of scrambling at least any puzzle in which every face has an opposite:
First, construct a checkerboard pattern in which every face alternates
pieces with its opposite, and then use random scrambling twists from
that state. That still doesn’t solve our need for a Goldilocks function,
but I bet that it would drastically reduce the number of needed
scrambling twists for many puzzles.


On 5/4/2011 9:50 AM, schuma wrote:
> Melinda,
> The official rule of WCA about scrambling can be found here:
> <>
> The rule specified which program to use to generate the scramble sequences, and the length of the sequences. They shouldn’t be too long coz that’s a burden for the scramblers.
> I think the most interesting case is 2x2x2. By simple brute force search, the god’s number is shown to be 11. The length of scramble sequences is random, according to the official program. The length is usually 7~9, which is less than the god’s number. Sometimes very short scramble sequence is generated from that program, like with length 5. Then the contestant will be lucky. And the record is still official. I think the reason they don’t use 11-move scrambling is because, with 9 moves most of the states (3 million out of 3.6 million states) can already be covered (see the table in So WCA feels it not necessary to use more moves.
> The scrambling rule for other puzzles is more intuitive. The length is always approximately the god’s number of an estimate of it, as far as I can see. For example, the length for 3x3x3 is about 20, 21.
> But I guess every one agrees that the complexity of a human solve has little to do with whether the puzzle is really fully scrambled or not, except it’s too easy. Like, nobody can take advantage from the fact that the 120-cell is scrambled by 1000 moves rather than 4000 moves.