# 5x5x5 intuitively/ blockbuilding method



## Am1n- (Jul 16, 2009)

I've been messing around with an intuitive blockbuilding method for the 5x5x5. I'm going to show the steps I did.

1: scrambled cube






2: building a 2x2x1 block




3: extending to 2x2x2




4: extending to 2x2x3




5: extending to 3x2x3




6: extending to 3x3x3




7: extending to 3x3x4




8: extending to 3x3x5




9: extending with a 3x3x1 block




10: extending with another 3x3x1 block




11: inserting a 3x1x1 block






12: I define the yellow layer as top layer and pair the top-layer thredges






13: Inserting the last bottom wing-edge and completing the last tredges




14: orienting and placing the tredges




15: finishing the 3x3x3 centers, commutator-based




16: finishing the last 5 corners, commutator-based ==> finished







Let me know what you think of this, should I work it out further? Has anyone tried something like this?...

mvg


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## 04mucklowd (Jul 16, 2009)

I dont know if it will be as good as reduction.

But, I guess it could be a method...


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## AvGalen (Jul 16, 2009)

Please provide a scramble and the moves that are needed to go from step to step.

For reduction, you need (roughly) 60 moves for centers, 80 for edges and 55 for 3x3x3 so about 200 in total.

If this method has a much higher move-count (I think it does) or a worse look-ahead (I think it does at least in the beginning) it is probably not worth it for speedsolving. It is fun as an alternative though


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## blah (Jul 16, 2009)

It is already possible to solve a 5x5x5 intuitively using either any known BLD method, or centers - AvG edges - Heise.

@04mucklowd and Arnaud: I don't think the OP intended it to be a speedsolving method. He just wanted to show a fun way of solving a 5x5x5


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## Zaxef (Jul 16, 2009)

That's cool!
As AvG said, please give us a scramble and the moves you use to solve it in this way!
(some pics like these would help too so we can follow along easily)


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## Am1n- (Jul 17, 2009)

So this is it:
scramble:
Rw' R D Bw2 Lw2 D' B2 Bw Uw' B' Fw' F' U2 Rw' R2 Dw' Rw' B' U' B' Fw' F2 R' Bw2 D Dw Uw2 U' Rw2 B' D2 B Bw' Fw F' Lw' Dw' Bw' L' Lw B' R Bw2 Dw2 B2 D' F' Rw' B2 F' D2 Dw' Uw U2 Bw' F U' Bw D U2

Solution:


2x2x1: D L' F2 L2 U' L2 U2 F' U (9 = 9)
2x2x2: U R2 D2 R U' (9 + 5 -1 = 13)
2x2x3: F' D F Fw' R2 Fw (6 + 14 = 19)
2x3x3: Rw Lw F Rw' Lw2 L' Rw' U' Rw (19 + 9 = 28)
3x3x3: D Dw'2 B Dw Uw R' Uw2 (29 + 8 = 36)
3x3x4: F U Lw' U'
Lw U Lw' U'

L2 Bw' L Bw D'
Fw D' Fw'(36 + 16 = 52)

3x3x5: F Dw F'
R' D R F D2 F'
Dw L U' F2 L' F2 L U
L' Uw2 R' D2 R Uw2 (52 + 23 = 75)

3x3x1 ext1: Fw' D' Fw D Lw2 D' Dw L' D
L B Dw' B'
D L D' Dw' Lw (75 + 18 = 93)

3x3x1 ext2: Dw' L D L2 D' L2
F B' L F' L' B
L D L' (Fw Bw') F' L F L' (Fw' Bw)
U { L' D L B D2 B'} U'
Uw { L' D L} Uw' (93 + 36 = 129)

(z2)

3x1x1 insertion: R Uw R' Uw' U
R Uw U' R'
(commutator) Rw R' U' Rw' Lw F Rw' R F' Rw Lw' U
(insertion) Uw Rw Uw' Rw' (129 + 24 = 153)

Tredge pairing: 
1: U [RU'R' F'UFU RU'R']
U2 [R (Uw2 U2) R' Uw']
[RUR'UF'U'F]
U2 [R (Uw2 U2) R' Uw']
2: R U2 R'
[RU'R' F'UFU RU'R']
U2 [R (Uw2 U2) R' Uw']
3: F' U2 F
U2 [R (Uw2 U2) R' Uw']
[RUR'UF'U'F] Uw
4: U F' U' F
U' [R (Uw2 U2) R' Uw']
[RUR'UF'U'F] Uw' (153 + 92 = 245)
Last tredge + bottom wing-edge: F' U2 F
Uw2 R U R' U

(F' U F) Uw' (F' U' F)

R Uw' R (245 + 18 = 263)

Orienting + placing tredges: R U' R U F' U' F
U R U R' U' R U2 R' U2 (263 + 16 = 279)

Center commutators: (279 + 170 = 449) ==> lol
corner commutators: +14: corner twist
+9: 3-cycle (here PLL case) (449 + 23 = 472)

==> sjiit: forgot parity +9 (472 + 9 = 481)



Can anyone check this???

mvg


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## Am1n- (Jul 17, 2009)

Ok, first,
I began to experiment with this because:
--> I have a 3x3x3 cube, I solve it as a 3x3x3.
--> I have a 5x5x5 cube, I reduce it to a 3x3x3 and then solve it as a 3x3x3. ==> first tought: FAIL
so now:
--> I have a 5x5x5 cube, I solve it as a 5x5x5.

It's indeed not a speedcubing method, but still, I like the idea. 

second,
The movecount is 481 moves for this previous example but there are some flaws in the solution and the solver:
1: I'm not a very good cuber (AvG: 5x5x5 reduction: 200 moves, me 300 moves).
2: The blockbuilding (ext2 3x3x5) probably can be done in much fewer moves (pulling together steps, more efficient blockbuilding, etc.)
3: The center commutators (170 moves!) I come to realize whilst I only use {F, R, U and Um} moves for the tredge pairing, I could make the top center before the tredgepairing, so I have more degrees of freedom( {F, Fw, R U, Uw} ), so much less moves. This means that the center commutators go down to a maximum of 135 moves (I think; my logic: 4 3x1 blocks and possible a 2x1 block of the last bottom wing-edge => choose the center with (max)5 wrong centerpieces as your last, which will be solved automaticly if the others are solved. That leaves 3*3 centerpieces that need to be solved with each max 1 commutator(with a conjugate of max 1) so that is 9*(1+13+1)=135).
4: While placing the tredges, I could also solve 2 corners using Heise (2 pairs or 1 pair) whilst now I use the (tr)edges first method (which isn't that efficient). That means the corner-commutators are down to 1 with a maximum of 12 moves (conjugate of 2, commutator of 8)
5: The parity (which in this case i forgot  ) probably can be solved with a little planning whilst making the last 2 tredges and inserting the last bottom wing-edge. (I'll experiment with this later on)

Maby I'll make another exaple, paying attention to the above points later.

PS: sorry for any mistakes in my spelling, I'm not very good in writing English 

mvg


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## Lucas Garron (Jul 17, 2009)

Am1n- said:


> Can anyone check this???


I get http://tinyurl.com/algDL-F2L2U-L2U


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## Am1n- (Jul 17, 2009)

Lucas Garron said:


> Am1n- said:
> 
> 
> > Can anyone check this???
> ...



Thanks I forgot 1 move (commutator for the 3x1 insertion after ext2)
I doesn't Work completely now, but I think you'll get the point.


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## Zaxef (Jul 17, 2009)

Very nice, I'll try this later, thanks for avoiding cube rotations lol


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## mrCage (Jul 19, 2009)

Hi 

With such a high move count it stands no chance as a top notch speeding method even with perfect lookahead. My cage method has about 300-350 turns (done slowly, so real count is a bit higher i guess). Cage method has almost "perfect" lookahead, at least for the later stages. I have achieved low 1:40 with this. Im no longer an active speedcuber, as my prime interests have changed.

Per


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## qqwref (Jul 19, 2009)

This sounds like a very fun method to play around with (I've tried similar ones for fun), but given the lookahead and number of moves required it's definitely not going to be a good choice for speedcubing, as people have said before.

If you want to solve the 5x5 more like a 5x5 and not just by reducing to a 3x3, I suggest Cage, sandwich (aka r5), K4, or my columns method.


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## Am1n- (Jul 19, 2009)

Thanks for the replies 

The movecount in this method can't be such a problem, I just did a quick solve with approximately 350-400 moves(counting the slice moves as 1, in the example I counted the slice moves as 2 (Rw R') ), but the lookahead isn't quite good (certainly in the beginning), but it betters as you solve more things (which is quite logical  ). But I still like solving ot this way because I'm no big algorithm fan, and here there arn't needed any, only the knowledge of commutators and some insight is needed (somewhat like Heise).

I'll certainly look up some of the other methods you mentioned

mvg


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## mrCage (Jul 19, 2009)

If you really enjoy making up on-the-spot commies (commutators) then cage is your friend.

Per


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## mrCage (Jul 29, 2009)

qqwref said:


> This sounds like a very fun method to play around with (I've tried similar ones for fun), but given the lookahead and number of moves required it's definitely not going to be a good choice for speedcubing, as people have said before.
> 
> If you want to solve the 5x5 more like a 5x5 and not just by reducing to a 3x3, I suggest Cage, sandwich (aka r5), K4, or my columns method.


 
Any more information about the sandwich/r5 method?? I can sorta guess it would do 2 opposite layers first... Google didnt give me anything:confused:

Per


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## TMOY (Jul 29, 2009)

My own variant: build 2 opposite centers, then the corners, then finish the opposite layers, then the middle edges, and finally the last 4 centers. If I remember correctly rachmaninovian's method is slightly different (after the first 2 centers, he solves the "3^3" formed by the corners and midges).
I tried a slow solve and got a move count of 156 STM (counting HTM makes no sense for such a method), but the solve was quite easy. The average is closer to 180-200 STM.


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## rachmaninovian (Jul 30, 2009)

mrCage said:


> qqwref said:
> 
> 
> > This sounds like a very fun method to play around with (I've tried similar ones for fun), but given the lookahead and number of moves required it's definitely not going to be a good choice for speedcubing, as people have said before.
> ...



hehe per that's me and you suggested the name sandwich. 

TMOY: i would have used something similar to yours if I did not suck at corners first for 3x3...


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## AvGalen (Jul 30, 2009)

Reduction (AVG and Bigcubes have about the same movecount) would be about 60 for centers and 80 for edges when done at full speed. When done slowsolving it should be more like 50+70


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