Square-1 Yoyleberry Method

[Gx Cuber]

yo carykh is awesome I cannot express my feelings!!

 

[luizborges]

I used to use this method before I learnt Vandenbergh! The coolest part is probably that you can do 4b using 3-cycle commutators, so the whole solve requires zero algorithms. (Fun fact: when I did this, I used slice moves on both the left and the right, which looked pretty weird to a classmate who was an experienced squanner.)

How do you do commutators on a Square-1? How can you create an intersection of A and B of just one piece/block?

 

[xyzzy]

How do you do commutators on a Square-1? How can you create an intersection of A and B of just one piece/block?

(Notation: R = /; L = y2 / y2; U = (2, 0); D = (0, 2).) [D' L D, R] is a 3-cycle. If you expand and rewrite it to use only normal slices, it becomes D' / U / U' / D /.

If you're asking about squan commutators in general (not in the context of the Yoyleberry method), (i) this is not the right thread to ask that question and (ii) that is a lot trickier because of the bandaged nature of the puzzle. Or if you mean comms once the puzzle is in cubeshape, well, just mess around with the puzzle for a while and you'll probably find something. M2 (which is 1,0/−1,−1/0,1) is a useful primitive since it does two 2-cycles on the edges.

 

[luizborges]

@xyzzy I was talking about the commutator you used. I tried it out, I understood how it worked, but I'm still baffled by the Sq-1 UNintuitiveness...

It is so hard to track pieces in it, that even your simple alg D' / U / U' / D / looks confusing when trying to swap 2 pieces (instead of doing a 3 cicle)... o_O

 

[Metallic Silver]

Cary Huang ;_;

 

[referee]

Was this ever developed fully? I understand that this site's emphasis is in speed solving and Yoyleberry might be bad for it, but it looks like a really cool way of solving it, both with the double reduction and solving non-square. (Vandebergh method is fine, but notation is a bit ugh, hehe).

 

[TyeDye]

Was this ever developed fully? I understand that this site's emphasis is in speed solving and Yoyleberry might be bad for it, but it looks like a really cool way of solving it, both with the double reduction and solving non-square. (Vandebergh method is fine, but notation is a bit ugh, hehe).

I believe that the only people that developed it, in creating alg sets and practicing with them, kept those to themselves. I have reached out to multiple people before to see if they would be interested in either sharing their previously compiled alg sets or helping with generating relavent algs for Yoyleberry, since Yoyleberry algs are pretty unique to just this method, since they are done out of cubeshape and I have never gotten responses from anyone as of yet. I am still interested in this method, not for it’s speedsolving use, but just for fun. I think it would be an interesting method if it was fleshed out further, I just do not have the resources or knowledge to achieve that by myself.

 

[Hazel]

Fun fact, the name of this method is a reference to the YouTube animated series Cary co-created and continues to work on, Battle for Dream Island.

 

[SoundBalloon]

I believe that the only people that developed it, in creating alg sets and practicing with them, kept those to themselves. I have reached out to multiple people before to see if they would be interested in either sharing their previously compiled alg sets or helping with generating relavent algs for Yoyleberry, since Yoyleberry algs are pretty unique to just this method, since they are done out of cubeshape and I have never gotten responses from anyone as of yet. (...)

Yes! Sorry for not answering, I simply haven't been online for a year. I did generate algs for Yoyleberry, more than three years ago, using a homemade software... You can find them here (the flavour text is in french but the algs are in standard notation):

Square-1 : méthode Yoyleberry

Portail francophone sur le Rubik's Cube

forum.francocube.com

Some disclaimers first:
- I am a newbie at Sq-1 (I do not know how to solve one, Yoyleberry or not )
- I struggle with domino reduction-type puzzles, and Yoyleberry is one of such.
- I suggested several methods, but most do not have any alg (yet?).

None of the variants striked me as "elegant", "intuitive" or "not alg-intensive" (like Roux L6E is, for example). I also have no idea if there is a way that involves a better look-ahead, more flexibility, and less moves.

 

[xyzzy]

If we could somehow combine steps 1 to 3 into a single edge pairing step (along with 1-looking step 4b), it might be pretty decent. I thought of generating algs for edge pairing, but then I got lazy and ended up learning Vandenbergh instead.

Sometimes it just takes four years to become less lazy, I guess. Saw this thread pop up again recently and decided to tackle this.

bobthegiraffemonkey's post earlier in the thread includes the distribution for getting to a shape where the edges are paired. This isn't enough for the Yoyleberry method, which also needs the edge pairs to be all white-yellow or all yellow-white. This is the actual distribution for directly pairing the edges into white-yellow or yellow-white pairs, weighted by frequency (slice metric):

0	586
1	640
2	6444
3	34648
4	69798
5	16558
6	56

Obviously, no one is going to learn the 2000-ish cases, but surely there's something better than cubeshape-EO-barrels… What other intermediate shapes could we use?

This is the average number of slices for optimally going from a certain shape into the paired state:

Spoiler

How to interpret this: left column is the average number of slices multiplied by 35. So "94" really means 94/35 = 2.69 slices average. There are a lot of symmetrically equivalent shapes that are left in because I didn't bother taking them out.

94 barrel/barrel
99 mushroom/mushroom
100 barrel/scallop,scallop/barrel
110 peacock/24,peacock/42,barrel/shield,shield/barrel,square/barrel,24/peacock,42/peacock,barrel/square
112 r.fist/barrel,l.fist/barrel,barrel/r.fist,square/r.fist,r.fist/square,l.fist/square,barrel/l.fist,square/l.fist
114 mushroom/l.paw,l.paw/mushroom,r.paw/mushroom,mushroom/r.paw
115 badge/15,badge/51,badge/33,15/badge,51/badge,33/badge
116 kite/mushroom,mushroom/kite
117 shield/shield
118 mushroom/r.fist,r.fist/mushroom,l.fist/mushroom,mushroom/l.fist
119 scallop/scallop,r.fist/r.fist,l.fist/l.fist
120 peacock/6,6/peacock
121 shield/scallop,peacock/222,scallop/shield,222/peacock
122 r.fist/scallop,l.fist/scallop,scallop/r.fist,scallop/l.fist
123 square/scallop,scallop/square
126 r.fist/shield,l.fist/shield,shield/r.fist,kite/r.fist,kite/square,shield/l.fist,kite/l.fist,r.fist/kite,square/kite,l.fist/kite
128 kite/l.paw,kite/r.paw,l.paw/kite,r.paw/kite
129 arrow/15,arrow/51,kite/kite,15/arrow,51/arrow
130 r.fist/l.paw,l.paw/r.fist,l.fist/r.paw,r.paw/l.fist
133 peacock/114,114/peacock
134 barrel/l.paw,l.paw/barrel,r.paw/barrel,barrel/r.paw
135 arrow/24,arrow/42,square/l.paw,square/r.paw,l.paw/square,r.paw/square,24/arrow,42/arrow
136 arrow/114,peacock/123,badge/123,peacock/132,badge/132,123/peacock,132/peacock,114/arrow,123/badge,132/badge
137 l.paw/l.paw,l.fist/r.fist,r.paw/r.paw,r.fist/l.fist
138 square/square
139 badge/114,arrow/123,arrow/132,shield/l.paw,l.paw/shield,r.paw/shield,kite/shield,shield/r.paw,shield/kite,123/arrow,132/arrow,114/badge
140 peacock/15,peacock/51,arrow/33,15/peacock,51/peacock,33/arrow
141 l.fist/l.paw,r.paw/r.fist,r.fist/r.paw,l.paw/l.fist
142 l.paw/scallop,r.paw/scallop,kite/scallop,scallop/l.paw,mushroom/barrel,barrel/mushroom,scallop/r.paw,scallop/kite
143 square/shield,kite/barrel,shield/square,barrel/kite
144 arrow/6,6/arrow
145 arrow/222,222/arrow
146 square/mushroom,mushroom/square
147 star/62,star/44,62/star,44/star
149 star/8,8/star
150 peacock/33,33/peacock
151 mushroom/scallop,r.paw/l.paw,scallop/mushroom,l.paw/r.paw
152 badge/24,badge/42,24/badge,42/badge
153 mushroom/shield,shield/mushroom
159 badge/6,badge/222,6/badge,222/badge
161 star/53,53/star
163 star/71,71/star

If you start in square-square, then the optimal way to get to paired edges is EO into barrels; there's no shortcut.

On the other hand, if you directly start in barrel-barrel, 1/35 of the time the edges are already paired, 9/35 you need two slices, 24/35 you need three slices, and 1/35 you need four slices. The second-best shape to start with, mushroom-mushroom, has the distribution 4/35 one slice, 7/35 two slices, 15/35 three slices, and 9/35 four slices.

But that's assuming your scramble is already in those specific shapes; barrel-barrel and mushroom-mushroom are actually the third- and fourth-worst shapes in terms of the average optimal slices to get there (both ~3.8 slices). So what we should actually be considering is: (average move count to get into xxx shape) + (average move count to go from xxx shape to paired edges). The distribution:

Spoiler

See above spoiler box for how to interpret this. This is now on a scale of 35×3678 = 128730, so e.g. "691826" really means 691826/128730 = 5.37 slices average.

691826 r.fist/scallop
703480 peacock/24
710880 badge/15
714336 r.fist/barrel
714658 r.fist/shield
719522 mushroom/l.paw
720724 mushroom/r.fist
734600 barrel/scallop
734880 arrow/24
735842 arrow/15
741894 kite/l.paw
747728 peacock/123
750904 peacock/114
764090 r.fist/l.paw
764318 badge/123
772412 arrow/123
772922 barrel/l.paw
776510 peacock/15
785712 shield/l.paw
788130 arrow/33
788250 barrel/shield
789528 kite/mushroom
789848 l.fist/l.paw
793296 square/r.fist
794040 badge/33
796938 arrow/114
797984 square/scallop
805588 kite/r.fist
810852 r.fist/r.fist
812776 l.paw/scallop
817632 badge/114
822440 peacock/6
822456 l.paw/l.paw
824292 scallop/scallop
824466 kite/scallop
826400 square/barrel
828872 barrel/barrel
833176 shield/shield
834132 arrow/6
834868 shield/scallop
837302 kite/shield
844710 square/l.paw
847192 mushroom/mushroom
854678 peacock/222
855290 peacock/33
867000 arrow/222
867578 r.paw/l.paw
879086 l.fist/r.fist
882534 square/shield
892396 badge/24
899894 kite/barrel
922038 mushroom/scallop
922128 square/mushroom
928536 star/62
930934 mushroom/shield
934066 star/44
941292 kite/kite
942152 badge/6
944726 mushroom/barrel
964208 kite/square
971522 star/8
979678 star/53
980442 badge/222
1006984 star/71
1102844 square/square

While it's conceptually easy to do the edge pairing starting with cubeshape, it's also literally the worst possible choice in terms of efficiency. Barrel-barrel and mushroom-mushroom fall from grace (6.44, 6.52 slices resp.), with fist-scallop taking top spot (5.37 slices).

Fist-scallop is second-best in terms of getting into the shape (1.89 slices), but pretty middling in terms of pairing (3.49 slices average; 4/35 two slices, 10/35 three slices, 21/35 four slices). The lack of symmetry also means you have to learn all 35 edge pairing cases separately, and you still have to be able to mirror them since leftfist-scallop and rightfist-scallop need different algs. (TODO: generate the algs and see what they're actually like you can wait four more years for that to happen)

Barrel-scallop takes the tradeoff in the opposite direction. Getting into barrel-scallop is worse than median (2.85 slices), but doing edge pairing from there is good (2.86 slices average; 1/35 already paired, 10/35 two slices, 16/35 three slices, 8/35 four slices). The barrel side has rotational symmetry, which cuts the number of cases to 21; if we further reduce by mirrors, there are only 16 cases left.

Spoiler: algs (mirrors not included (yet))

These are for barrel on top, scallop on bottom, with the scallop edges facing you (set up with /-3,-3/0,1/0,-4/3,0). Images are generated with AlgDb's squan image generator, so the bottom face is shown from a top-down view (i.e. will look mirrored compared to tilting the cube upwards to look at the bottom face).

Cases are labelled with 8 binary digits; the first four are the edges on the barrel side, read clockwise from the front-right; the second four are the edges on the scallop side, from front-left to front-right (clockwise on the actual puzzle, anticlockwise in the AlgDb pics).

01 01 0101

skip!

00 00 1111

/ (5,0) / (0,-4) / (0,5) /
end shape: barrel-scallop

00 01 0111

/ (5,0) /
end shape: barrel-barrel

00 01 1101

(0,2) / (5,0) /
end shape: 42-peacock

00 01 1011

(5,0) / (0,-5) / (1,-1) /
end shape: barrel-scallop

00 01 1110

(-5,0) / (-1,0) / (-1,1) /
end shape: scallop-barrel

01 10 1100

/ (-1,1) /
end shape: scallop-barrel

01 10 1001

/ (5,1) / (-1,0) /
(6,0) / (5,1) / (0,1) /
end shape: barrel-barrel (for both algs)

01 10 1010

/ (-1,0) / (1,0) /
end shape: barrel-scallop

00 11 0011

/ (-1,1) / (2,0) / (0,5) /
end shape: peacock-42
(6,0) / (-1,1) / (-2,0) / (-5,0) /
end shape: peacock-24

00 11 0101

(1,0) / (-1,0) / (5,0) /
end shape: barrel-barrel

00 11 0110

/ (5,0) / (0,-4) / (5,0) / (note: same alg as 00 00 1111!)
end shape: barrel-scallop

01 01 1010 (paired, but not)

(1,0) / (-1,0) / (5,1) / (-1,0) /
end shape: barrel-barrel

01 01 0011

/ (-1,0) / (0,1) /
end shape: scallop-barrel

01 01 1100

(1,0) / (-1,-4) / (0,5) /
(1,0) / (5,2) / (5,0) /
end shape: 42-peacock (both algs)

01 01 0110

/ (0,1) / (0,5) / (0,-1) /
end shape: barrel-barrel

01 01 1001

/ (-1,0) / (0,-5) / (1,0) /
end shape: barrel-barrel

 

[abunickabhi]

Super interesting method. Thanks for presenting the stats, xyzzy!