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4x4x4 with only two alg's?

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#21
What 5x5 algs are there and can you explain them?
hopefully this wasnt answered already, but there are many cases for the last 2 edge groups. they all can be solved with a minimum of 2 algs, a parity fix and a edge swap, however there are many easy algs to optimize the solution of the last 2 edges for speed. they can be applied to any big cube with grouping slices or using single slices. .

http://www.bigcubes.com/5x5x5/lastedges.html
 
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#22
I avoided learning 4x4x4 algs for a year or more, then when I finally learned them, it was SO easy. I learned all 3 in a day, they were all much less effort than most PLLs.

You basically need 1 alg for the last 2 edges, then 1 alg for OLL parity, then 1 alg for PLL parity.

I think some of the algs that people typically use really suck.
I found these that work really well for me:
- Last 2 edge pairs: (Uu)' R U R' U' y' R' U R (Uu)
- OLL Parity: (Rr)' U2 (Rr) U2 (Rr)' F2 (Rr)2 U2 (Rr) U2 (Rr)' U2 F2 (Rr)2 F2 [seems long, but its really easy]
- PLL Parity: r2 U2 r2 (Uu)2 r2 (Uu)2 [you can replace the r2's with (Rr)2 R2 if you like]
 
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cyoubx
#23
I don't consider the 2 edge pairing an algorithm. You're basically just slicing, flipping the dedge, then slicing back. Quite intuitive actually.
 

JyH

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#25
All I use is the algorithms to pair the last two edges, OLL parity, and PLL parity. They're VERY easy algorithms to learn, you can probably learn the ones I use in about 5-8 minutes.
 
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#26
I could never figure it out intuitively, so I'll assume most people who don't want to learn algs probably can't either.
Heh, I agree. Though I suppose if I tried forever and ever, I could have eventually... but I didn't want to go for that. I just learned the two algs, one to orient one edge pair and the other to permute two pairs. Both were far easier to learn (very easy) than trying to figure it out.

Pairing all the edges before OLL is definitely intuitive though. Didn't need any algs for this.
 
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4EverTrying
#28
The simplest odd permutation on wing edges is a single inner layer quarter turn. Now, this has some effects on the centers, but fixing them is the intuitive challenge :)
Attacking the problem head on, using the approach of single sliced turn based single edge flip algorithms, the following algorithm may be the easiest to understand for the case of the "single edge flip."

[1] Start with this commutator to swap three 1x1x(n-1) blocks,
U2 l U2 r' U2 r U2 l'
Why this one and not its inverse? (As an obvious counterexample).
Because it doesn't discolor all three of the 1x(n-2) center blocks it affects. That is, it doesn't discolor the 1x(n-2) center block in the left half of the U layer.

[2] Add F2 to have all three wings in the same slice
U2 l U2 r' U2 r U2 l'
F2


[3] Add r, the quarter turn to solve back one 1x1x(n-1) block and induce the odd permutation.
U2 l U2 r' U2 r U2 l'
F2
r


[4] Add F2 to restore the cube somewhat
U2 l U2 r' U2 r U2 l'
F2
r
F2


[5] Add the following piece to pair up the remaining edges
U2 l U2 r' U2 r U2 l'
F2
r
F2
r' F2 r


[6] Add F2 to restore the cube somewhat
U2 l U2 r' U2 r U2 l'
F2
r
F2
r' F2 r
F2


[7] Add the non-center preserving PLL parity algorithm
U2 l U2 r' U2 r U2 l'
F2
r
F2
r' F2 r
F2
r2 F2 r2 F2 r2


This is a 20 btm algorithm. However, we can make an obvious change to promote a move cancellation to 19 btm.
U2 l U2 r' U2 r U2 l'
F2
r
F2
r' F2 r
r2 F2 r2 F2 r2
F2


Using the commutator F' r' F U2 F' r F U2, we can achieve an 18 btm which is nearly <U, r>:
r2 U2 r2 U2 r U2 r U2 r' U2 B2 U' r' U B2 U' r U'
 

AvGalen

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arnaudvg
#29
Heh, I agree. Though I suppose if I tried forever and ever, I could have eventually... but I didn't want to go for that. I just learned the two algs, one to orient one edge pair and the other to permute two pairs. Both were far easier to learn (very easy) than trying to figure it out.

Pairing all the edges before OLL is definitely intuitive though. Didn't need any algs for this.
what if you used an alg like "slice R U2 R' , F' U' F unslice" or "slice R U' R', F' U2 F unslice". that should make that "flipping" entirely intuitive.
Also, for 5x5x5 edges you only need a 3-cycle of edges (for the first 22 semi-pairs) and a parity-fix (for the last 2 IF you have parity)
 
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