Calculating Probabilities

[grsbmd]

Is there an easy way to calculate permutation probabilities for cases on a general puzzle?

I've seen it done using symmetries on the 3x3x3, but I'm interested in calculating probabilities for edge perm cases on the square 1.

 

[cmhardw]

Hey, which cases do you mean, or at least what is an example? Also do you mean when the puzzle is already in cube shape?

Let me know an example, or a little more detailed what you need and I can try to help out.

Chris

 

[pjk]

Calculating probabilities depends on what puzzle it is, as each one is calculated depending on the number of situations there may be.

 

[grsbmd]

What I'm interested in is calculating the probabilities for the cases like the ones on this page:

http://www.cubezone.be/square1step5.html

And everything is in order on the cube except for the edges.

 

[mmwfung]

Assume that one layer, say the bottom layer, is solved. Then there are 10 different cases with these probabilities:

Solved case : 1/24
(UF UB)(UL UR): 1/24
(UF UL)(UB UR): 2/24
(UL UB UR) : 4/24
(UR UB UL) : 4/24
(UF UR) : 4/24
(UL UR) : 2/24
(UF UL UR UB) : 4/24
(UF UL UB UR) : 1/24
(UF UR UB UL) : 1/24

Of course the same probabilities if the upper layer is solved instead of the bottom layer. So to calculate the probability of each edpermutation you must multiply the "probability of the U-layer" with the "probability of the D-layer". For example: (UF UL UB UR) (DL DR) has probability (1/24)*(2/24).

Correct me if something is wrong in this post.

Michael Fung

 

[grsbmd]

Yeah, that's the math that didn't add up for me. I assumed that the 7th case had rotational symmetry and therefore a mirror image (I didn't realize it could be obtained by a rotation)

I think I have it now.

 

[grsbmd]

New Question:
How would you calculate the probabilites for the shapes?