Random 20 move scramble

[IQubic]

If 20 is god's number, I wonder what the chance is of a completely random 20 QTM scramble, gettiing you the Superflip pattern (all edges fliped incorrectly). My way of getting a random scarmble is this: Pick a random number 1 - 18.
1. F
2. F'
3. F2
4. R
5. R'
6. R2
7. U
8. U'
9. U2
10. L
11. L'
12. L2
13. B
14. B'
15. B2
16. D
17. D'
18. D2
Find the number you picked and preform that move, now pick another number 1 - 18, do that move, then repeat until 20 moves have been done. If you have a better way of getting a random scramble then please share.

 

[cannon4747]

http://www.cubetimer.com/
and then i just press spacebar every time i want a new one...
for serious timing though, id use this:
http://cubemania.org/

 

[AustinReed]

Humans are never random. That's not going to be a "random" scramble.

Plus, what if you pick 16, then 18?

 

[qqwref]

If 20 is god's number, I wonder what the chance is of a completely random 20 QTM scramble, gettiing you the Superflip pattern (all edges fliped incorrectly).

Pretty low. You'd have to know the exact number of 20-move superflip solutions to calculate this though.

In general, if you scramble with 20 random moves, positions that require 20 moves are much less likely than positions that can be solved in fewer moves. If you're going to generate random moves, you should absolutely use more than 20 moves. 25 moves is typical.

My way of getting a random scarmble is this: Pick a random number 1 - 18. [...] Find the number you picked and preform that move, now pick another number 1 - 18, do that move, then repeat until 20 moves have been done. If you have a better way of getting a random scramble then please share.

This is an extremely poorly thought out method since it is very likely to give you moves that can be easily combined, such as B B2 or L R L. Any acceptable scrambling program will use a better method where those sequences aren't allowed. And a *good* scrambling program won't generate random moves, but will actually choose a random position and then give you a sequence of moves that gets there.

 

[IQubic]

Okey, so any better ways? As for my method, I thought of it in 20 minutes, so the flaws have not been worked out

 

[Ranzha]

It would be (# of 20-move superflip solutions)/(# of 20-move sequences)

 

[ben1996123]

gods number is 24qtm iThink.

 

[IQubic]

gods number is 24qtm iThink.

So 20 is another metric?

 

[ben1996123]

So 20 is another metric?

20 is HTM

 

[JonnyWhoopes]

So 20 is another metric?

[wiki]HTM[/wiki]

Also see [wiki]Metric[/wiki].

 

[qqwref]

Okey, so any better ways?

Just use the standard way everyone else uses. This problem has been solved for years. Look at the code of basically any scrambler.

 

[whauk]

if you find one solution you can easily create 960 using symmetries (some of them might be the same though).
factor 24 by conjugating with cube rotations, factor 2 by inverting the sequence, factor 20 by cycling the moves (or if you like this better: conjugating with the inverse of some moves at the beginning (which then obviously cancels out))

so i guess the number of superflip solutions is significantly higher than any other position with distance 20 from solved.


EDIT: i also do not understand why everyone wants to block the "hidden identities/shortcuts" in the move sequence. its very unlikely that you get a position that really requires 20 moves to solve in the end, so what is the point of filtering 1- or 2-move identities?

imo the number (#20-move-sequences that solve 20-move positions)/(#20-move-sequences that solve the superflip) is far more interesting. (and probably unsolvable without using computers)

 

[rokicki]

gods number is 24qtm iThink.

We know of a position that requires 26 moves in the quarter turn metric to solve,
so it must be at least 26.

 

[CubeRoots]

theres more than superflip thats 20 moves away. superflip is just the famous one

 

[ben1996123]

theres more than superflip thats 20 moves away. superflip is just the famous one

iirc there are about 300 million 20HTM positions.

 

[cuBerBruce]

if you find one solution you can easily create 960 using symmetries (some of them might be the same though).
factor 24 by conjugating with cube rotations, factor 2 by inverting the sequence, factor 20 by cycling the moves (or if you like this better: conjugating with the inverse of some moves at the beginning (which then obviously cancels out))

Superflip has all 48 symmetries of the cube, not just the 24 pure rotational symmetries. So you can also use mirroring. This would seem to make a multiplying factor of 48*2*20 = 1920. Because of adjacent commuting moves, I believe you can get more than a factor of 20 from cyclic shifting. I also note that arbitrary cyclic shifting only works because superflip commutes with every other position.

Mike Reid's web site claims that there are only two "distinct" optimal maneuvers for superflip in face turn metric:

U R2 F B R B2 R U2 L B2 R U' D' R2 F R' L B2 U2 F2 (20f*)
U R2 F B R B2 R U2 L B2 R U' D' R2 F D2 B2 U2 R' L (20f*)

It may be an interesting project to see exactly how many distinct variants you can produce from these two maneuvers.

 

[qqwref]

Don't forget we can also invert the sequences

 

[cuBerBruce]

Don't forget we can also invert the sequences

We didn't. symmetries: 48, inversion: 2, cyclic shift 20.

 

[qqwref]

Ah, okay. So are we sure those two are the only ones up to symmetries?

 

[IQubic]

So, hiw many ways to get Superflip? Would there be 43 Quintillion 20 move, because every scramble takes at least 20 moves to solve.