# Length of 2x2 Scrambles

#### cubernya

Mods: I have no clue if this should be in a thread, or in a different section. Just move this to where it belongs Thanks in advance

I was just wondering if someone could modify the Mark2/WCA 2x2 scrambler to make a count of how long the scrambles are. I am doing a project for college, and part of my choice was the length of proper scrambles. This would allow me to generate a large number of scrambles (10,000 probably) and have the length with the number of scrambles at that length next to it.

In case you don't see what I'm saying, I basically want the normal scrambler, but with a count at the bottom that shows (Length: # with length / 0: # / 1: # / 2: # / etc.)

If anybody could do this, it would be great. I tried to do this and failed

#### qqwref

##### Member
Yeah, I wasn't really sure what the difference was between this question and that table...

#### cubernya

Are the scrambles optimal? I thought they were near optimal. Regardless, if at all possible, I would like this done, as I am doing this project on what actually occurs, not just the theory (theory being the table, reality being the 10,000+ scrambles)

#### Lucas Garron

##### Member
1,000,000 runs of Mark 2 (which still uses the WCA 2x2x2 scrambler):

Code:
[0,4,14,79,539,2733,13832,62536,237605,513059,169008,591]
That's 0 at depth 0, 4 at depth 1, etc.

Simple hack of the benchmark code. It's not very robust, else I would make it a more general tool.
(Hopefully, this will all be very easy some day.)

(Ooh, matrix plot.)

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#### cubernya

1,000,000 runs of Mark 2 (which still uses the WCA 2x2x2 scrambler):

Code:
[0,4,14,79,539,2733,13832,62536,237605,513059,169008,591]
That's 0 at depth 0, 4 at depth 1, etc.

Simple hack of the benchmark code.
So basically the conclusion from this and the reality results are that it tends to lean away from longer scrambles, correct?

#### Lucas Garron

##### Member
So basically the conclusion from this and the reality results are that it tends to lean away from longer scrambles, correct?
Huh? The distribution matches perfectly.
(Did you note that my sample has a million runs, not 3672160?)