Discussion in 'Puzzle Theory' started by CubesOfTheWorld, Apr 8, 2010.

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1. ### TipsterTricksterMember

oh yea good point

2. ### CuberFlesMember

6
0
Sep 17, 2017
What are the odds for hitting edge parity on a 4 x 4? I'd say 40 %, since there are 5 possible situations after F3L (0, 1, 2, 3 or 4 dedges flipped) and only 2 of these are "wrong" (1 and 3). However, after several dozens of solves I can't seem to get any less than a 60 % chance to hit edge parity. I'm using the 3 x 3 reduction method (centers first, then pair the edges, then solve like a 3 x 3). Is my method invoking unfair amounts of parity cases? Is there anything I can do to hit parity less frequently?

3. ### obelisk477Member

Call the UB edge 1, the UR edge 2, the UF edge 3, and the UL edge 4, for the sake of this discussion. Now let us consider the ways that you can have parity.

0 Edges
1,2,3,4 are flipped - NO PARITY

1 Edge
1 is flipped - PARITY
2 is flipped - PARITY
3 is flipped - PARITY
4 is flipped - PARITY

2 Edges

1 and 2 are flipped - NO PARITY
2 and 3 are flipped - NO PARITY
3 and 4 are flipped - NO PARITY
4 and 1 are flipped - NO PARITY
1 and 3 are flipped - NO PARITY
2 and 4 are flipped - NO PARITY

3 Edges

1 is not flipped - PARITY
2 is not flipped - PARITY
3 is not flipped - PARITY
4 is not flipped - PARITY

4 ֵEdges

All four are not flipped - NO PARITY

If you count up each of the 'Parity' and 'No parity', you'll see that the split is 50%. The fact that you're seeing 60% is just unfortunate, and over a long number of solves, you'd see it settle to 50%.

4. ### CuberFlesMember

6
0
Sep 17, 2017
Aha, thanks for pointing that out

24
13
Aug 13, 2017

6. ### Oliver1010Member

24
13
Aug 13, 2017
What are the odds of a last layer skip, oll skip, or pll skip on a 4x4 or even layered cube

7. ### xyzzyMember

980
487
Dec 24, 2015
OLL skip: 1 / (2^4 3^3) = 1/432
Full PLL skip: 1 / (4! 4!) = 1/576
PLL skip (allowing for AUF): 4 / (4! 4!) = 1/144
Full LL skip: (1/432) (1/576) = 1/248832
LL skip (allowing for AUF): (1/432) (1/144) = 1/62208

8. ### 94mattMember

1
0
Oct 5, 2017
HI guys just want to know that if you have all the corners and one side completed, how many possibilities do you have for the last 8 egdes?

9. ### TDMSuper ModeratorStaff Member

6,987
243
Mar 7, 2013
Oxfordshire, UK
WCA:
2013MEND03
TDM028
There are 8!/2 possible permutations and 2^7 possible orientations of the last eight edges. Multiplying those gives a total of 2,580,480 cases.

10. ### guysensei1Member

5,101
449
Nov 24, 2013
Singing pores
WCA:
2014WENW01
This only works if you are considering rotated versions of the same case as distinct. For example there are 8 'ways' for a clockwise U perm to appear that fits OP's description.

TDM likes this.
11. ### Duncan BannonMember

883
190
Sep 9, 2017
Here
Most of the people here probably know this, but the chance of a PLL skip is the same as getting a H perm. 1/72

Also, how many algs would there be for FULL 1LLL

12. ### Rubix CubixMember

154
37
Jul 24, 2016
Bath, UK
WCA:
2016GLOZ01
If you want to do 1LLL, then you could learn ZBLL, only 493 cases I think

13. ### ErwinOlieMember

14
9
Oct 4, 2017
Gouda, The Netherlands
WCA:
2014OLIE01
The wiki gives the number 3915 with full explanation where that number comes from.
https://www.speedsolving.com/wiki/index.php/1LLL

14. ### Duncan BannonMember

883
190
Sep 9, 2017
Here
Okay, Thanks!

15. ### Duncan BannonMember

883
190
Sep 9, 2017
Here
What are the chances of a no AUF PLL skip for 2x2? Thanks

16. ### TDMSuper ModeratorStaff Member

6,987
243
Mar 7, 2013
Oxfordshire, UK
WCA:
2013MEND03
TDM028
Probability of CP skip: 1/6
Probability of AUF skip: 1/4
Total probability of AUFless PLL skip: 1/24.

17. ### Duncan BannonMember

883
190
Sep 9, 2017
Here
Sweet, You the man, thanks.

Edit- that was really easy math Duncan, LOL
Edit2- Is the chance of PLL skip really 1/6? Because of the H cases wouldn’t it be 6/30?
Edit3- What are chances of full No AUF LL skip on 2x2? Thanks

3,410
20
Dec 15, 2012
Finland
WCA:
2013JOKI01
TheUnknownCuber
Yes, there are 4! ways to permute the four corners. Four of them are "solved" (disregarding AUF). 4!/4 = 3! = 6, hence 1/6

Similarly, there are 4! different ways to arrange four corners when they are oriented. Only one of them is completely solved, thus PLL skip with no AUF is 1/24

19. ### Duncan BannonMember

883
190
Sep 9, 2017
Here
Oh, very cool. Thanks.

20. ### CornerCutterMember

What is the probability of getting a 6 move Pyraminx scramble?