The 3x3x3 Example Solve Thread

Renslay said:
Good old Roux solve.

 Twizzle link 
 Setup 
L2 R2 B F2 R2 F' D2 L2 F' L2 D' L R2 D B U' F' L' D U
 Moves 
z'
B2 F' L' F R U2 R U' B // FB
U R2 U M' U2 R2 U' R2 U2 R U' r' // SB
U' R2 D' R U2 R' D R U2 R // CMLL
M' U' M' U2 M' U M // EO
U' M U2 M' U M' U2 M' // LSE

Next: L2 B2 L2 F' L2 U2 R2 D2 F U2 L2 B' R' D2 R' B' L' U R' D2 B
Click to expand...
Aurora II, 52 moves, not bad

 Twizzle link 
 Setup 
L2 B2 L2 F' L2 U2 R2 D2 F U2 L2 B' R' D2 R' B' L' U R' D2 B
 Moves 
y2 // inspection
l U F' U2 L2 F' R U r2 U r' //223 (11/52)
y U L' U' L F' U2 F' //fs (8/52)
U2 R U R' U2 S' R U' R' S //peopair (10/52)
U R U R' U R U' R' F' //rfcp (9/52)
R U R2 U' R2 U' R2 U2 R U' R U' R' U2 // 2gll (14/52)

Next: R B' D2 F L2 R2 U2 R2 B' D2 L F' D2 B2 L' D L2 F' U2
 
Renslay said:
<U2,D2,R2,L2,F2,B2> and <U,D,R,L,F,B> are not the same. The <.> notation indicates a generator:
en.wikipedia.org

Generating set of a group - Wikipedia

en.wikipedia.org en.wikipedia.org

For example, <R, U> means, by definition, "the smallest subgroup of the cube group that contains R and U". And since every subgroup is also a group, that means all sort of inverse and concatenation moves are included: R, R U, R' U2 R U', etc.

In practice, <U2,D2,R2,L2,F2,B2> means "all state that I can reach by doing half-turn".
And <U,D,R,L,F,B> means "all state that I can reach by doing quarter-turns."

U2,D2,R2,L2,F2,B2> means the cube is in a state which can be (but not necessary have to be) solved only half turns.
<U,D,R,L,F,B> means... well, ANY cube state, since we can reach any state with quarter turns.

Yes, you can do a half turn by repeated quarter turns, but the reverse is not true.

Also, fun fact, <U,D,R,L,F,B> is not even the smallest generator. <D,R,L,F,B> is smaller as a generator, but it represents the same subgroup: the entire cube state. That is because you can show that a single U turn can be reached by using D,R,L,F and B moves:
U = F B L2 R2 F' B' D' B F R2 L2 B' F'

 Twizzle link 
 Setup 
U
 Moves 
F B L2 R2 F' B' D' B F R2 L2 B' F'


You can show that you cannot reduce the generator further if you only consider outer side turns.
Practice for the readers:
1) show that not every cube state are in <D,L,F,B>, i.e., not every cube can be solved using only D, L, F and B moves. (easy)
2) show that not every cube state are in <R,L,F,B>, i.e., not every cube can be solved using only R, L, F and B moves. (slightly harder)

The smallest generator for the cube is by the way only a set of two elements! (But they are not single outer side turns). Although it was not easy to find / prove:
Lucas Garron

Thread 'The entire cube is 2-gen!'

By which we mean the cube group can be generated by 2 elements:

G = <g1, g2> = <U B L U L' U' B', R2 F L D' R'>

So, any position of the cube can be written as something like \( g1 g2^2 g1^{-1} g2^3 \), except longer.

Apparently this was known in 1980. Joyner cites this set by "F. Barnes" in a book by Bandelow (which I have yet to see).

I believe this, but I'd like to see a proof by generating each of {B, F, U, D, L, R} as an "alg" in <g1, g2>. (Or at least 5 of them.)

ksolve can't quite handle this. Since 4.3*10^19 is about 65 binary digits...
Click to expand...

Perhaps you missed my point.

In this post I was reffering to your solution, for instance this part:

"
[...] // <U,D,L2,R2,F2,B2> corners
F2 U R2 U R2 U' R2 U2 R' F R' B2 R F' R U' [...]
"

where you were trying to say that the corners-state prior the move sequence on line 2 can be made half-turn solvable using the generators listed on line 1.

I was wondering why you didn´t write

"
[...] // <U,D,L,R,F,B> corners
F2 U R2 U R2 U' R2 U2 R' F R' B2 R F' R U' [...]
"

instead because all your criteria mentioned in this post would still be met as stated in the first link above.
 
CrossPetrus said:
Aurora II, 52 moves, not bad

 Twizzle link 
 Setup 
L2 B2 L2 F' L2 U2 R2 D2 F U2 L2 B' R' D2 R' B' L' U R' D2 B
 Moves 
y2 // inspection
l U F' U2 L2 F' R U r2 U r' //223 (11/52)
y U L' U' L F' U2 F' //fs (8/52)
U2 R U R' U2 S' R U' R' S //peopair (10/52)
U R U R' U R U' R' F' //rfcp (9/52)
R U R2 U' R2 U' R2 U2 R U' R U' R' U2 // 2gll (14/52)

Next: R B' D2 F L2 R2 U2 R2 B' D2 L F' D2 B2 L' D L2 F' U2
Click to expand...
This is the best I got...
 Twizzle link 
 Setup 
R B' D2 F L2 R2 U2 R2 B' D2 L F' D2 B2 L' D L2 F' U2
 Moves 
z2 // Inspection
F L' U' L U R U' R U R2 F R F' y2 // F2S+LEFI
R2 U R' U2 S' U S // EO
// L2DE Skip which is 1/56
U R U2 R' U2 R U R' // Numann First Look
U2 R' U2 R // Numann Second Look
U' R D R' U' R D' R2 U2 R // Numann Third Look
R U R' U' D R2 U' R U' R' U R' U R2 D' U' // PLL

Next: L2 F2 L2 B2 U2 F R2 U2 F' R2 B' D' L U' L2 B F L R2 D' B
 
bcube said:
Perhaps you missed my point.

In this post I was reffering to your solution, for instance this part:

"
[...] // <U,D,L2,R2,F2,B2> corners
F2 U R2 U R2 U' R2 U2 R' F R' B2 R F' R U' [...]
"

where you were trying to say that the corners-state prior the move sequence on line 2 can be made half-turn solvable using the generators listed on line 1.

I was wondering why you didn´t write

"
[...] // <U,D,L,R,F,B> corners
F2 U R2 U R2 U' R2 U2 R' F R' B2 R F' R U' [...]
"

instead because all your criteria mentioned in this post would still be met as stated in the first link above.
Click to expand...

When I wrote "<U,D,L2,R2,F2,B2> corners", I meant "solving the corners to bring the cube (closer) to the <U,D,L2,R2,F2,B2> state".

Imagine someone using a beginner method, and writes:
[some moves] // first layer corners
[more moves] // first layer edges

Here, "first layer corners" mean they did something with the corners so the cube got closer to a state where the first layer is solved.

This is the logic I followed.
 
CrossPetrus said:
Next: R B' D2 F L2 R2 U2 R2 B' D2 L F' D2 B2 L' D L2 F' U2
Click to expand...

I know acrystal already wrote a solution, but I was in the middle of one too, and I don't want it to be wasted. :)

So, here is a strict Human Thistlethwaite Algorithm, where I truly restricted the movements of one state to that's state generator movements.

 Twizzle link 
 Setup 
R B' D2 F L2 R2 U2 R2 B' D2 L F' D2 B2 L' D L2 F' U2
 Moves 
z'
R' L F D F' R' F // <U,D,L,R,F2,B2>
D L' U2 R'
D2 F2 U' R U R' U R U2 R' // <U,D,L2,R2,F2,B2>
F2 U F2 L2 U L2 U' L2 B2 U' B2 U B2 U2
R2 L2 D' F2 U R2 L2 D' // <U2,D2,L2,R2,F2,B2>
U2 F2 U2 R2 F2 R2 F2
B2 R2 D2 F2 D2 F2 D2 F2 R2 B2 R2 // <>


Next (copied from acystal): L2 F2 L2 B2 U2 F R2 U2 F' R2 B' D' L U' L2 B F L R2 D' B
 
Last edited:
Renslay said:
I know acrystal already wrote a solution, but I was in the middle of one too, and I don't want it to be wasted. :)

So, here is a strict Human Thistlethwaite Algorithm, where I truly restricted the movements of one state to that's state generator movements.

 Twizzle link 
 Setup 
R B' D2 F L2 R2 U2 R2 B' D2 L F' D2 B2 L' D L2 F' U2
 Moves 
z'
R' L F D F' R' F // <U,D,L,R,F2,B2>
D L' U2 R'
D2 F2 U' R U R' U R U2 R' // <U,D,L2,R2,F2,B2>
F2 U F2 L2 U L2 U' L2 B2 U' B2 U B2 U2
R2 L2 D' F2 U R2 L2 D' // <U2,D2,L2,R2,F2,B2>
U2 F2 U2 R2 F2 R2 F2 R2
R2 B2 R2 D2 F2 D2 F2 D2 F2 R2 B2 R2 // <>


Next (copied from acystal): L2 F2 L2 B2 U2 F R2 U2 F' R2 B' D' L U' L2 B F L R2 D' B
Click to expand...
Ill guess Ill use this as FMC practice
and domino effect ahh cross
 Twizzle link 
 Setup 
L2 F2 L2 B2 U2 F R2 U2 F' R2 B' D' L U' L2 B F L R2 D' B
 Moves 
z2 // Inspection
D' L' F' R' B' // Cross
U' R U R' // 1st Pair
U' B2 R B2 R' // 2nd Pair
y2 U' D' R U R2 F R F' D // 3rd Pair
F' U2 F U2 F' U' F // 4th Pair
y R U2 R2 F R F' U2 Rw R' U R U' Rw' // OLL
y' R U R' U' R' F R2 U' R' U' R U R' F' U' // PLL

Next: D2 F' L2 R U' D L2 D B U2 L2 R' D L2 F2 R U R U L2 D' F' U' B2 R2
 
acrystal said:
Next: D2 F' L2 R U' D L2 D B U2 L2 R' D L2 F2 R U R U L2 D' F' U' B2 R2
Click to expand...

 Twizzle link 
 Setup 
D2 F' L2 R U' D L2 D B U2 L2 R' D L2 F2 R U R U L2 D' F' U' B2 R2
 Moves 
U' F2 r' u' R' u2 M B M' r B' // FB
U' M' U' R' U R' U' r U' r' U2 r U R' // SB
R U2 R' U' R U' R2 U2 R U R' U R // CMLL
U' M U2 M' U2 M U2 M2 U M U2 M U2 M' // LSE


Terrible scramble for my usual Roux colors. :/

Next: L B' U' L' D B2 U2 F' L' R2 U L2 F2 U' R2 F2 D2 F2 U' L2 F'
 
Renslay said:
 Twizzle link 
 Setup 
D2 F' L2 R U' D L2 D B U2 L2 R' D L2 F2 R U R U L2 D' F' U' B2 R2
 Moves 
U' F2 r' u' R' u2 M B M' r B' // FB
U' M' U' R' U R' U' r U' r' U2 r U R' // SB
R U2 R' U' R U' R2 U2 R U R' U R // CMLL
U' M U2 M' U2 M U2 M2 U M U2 M U2 M' // LSE


Terrible scramble for my usual Roux colors. :/

Next: L B' U' L' D B2 U2 F' L' R2 U L2 F2 U' R2 F2 D2 F2 U' L2 F'
Click to expand...
Just made a new method, Aurora III. This is its first solve, with 40 moves!!

 Twizzle link 
 Setup 
L B' U' L' D B2 U2 F' L' R2 U L2 F2 U' R2 F2 D2 F2 U' L2 F'
 Moves 
z2 //inspection
L' U' L2 U2 L' U' F' r' U2 r' U2 r2 //223 (12/40)
U' R2 U2 R2 U2 F R' F' //dfR square (8/40)
F' U2 F // pair (3/40)
R f R' U R U' R' f' //rf2g (8/40)
R' U2 R2 U R2 U R2 U2 R' //2gll (9/40)


Could be 39 moves with a cancel between dfR and pair, but 40 moves is great to start out with!
Next: L U2 F2 L' B2 L2 U2 B2 R' D2 F2 L B' F L' B' R F2 D' U R2
 
CrossPetrus said:
Next: L U2 F2 L' B2 L2 U2 B2 R' D2 F2 L B' F L' B' R F2 D' U R2
Click to expand...

 Twizzle link 
 Setup 
L U2 F2 L' B2 L2 U2 B2 R' D2 F2 L B' F L' B' R F2 D' U R2
 Moves 
y z'
b R2 b' U' B2 U' R B' // FB
U' r U R' U' F' U' F // CP
r' U r R U2 r U r' // EO
U' M2 U r2 // 223
R' U R U' R2 U R' U' R U2 R' U R // F2L
U' R' U2 R2 U R U R U' R' U' R2 U R U2 // 2GLL


I did a CEOR, a.k.a. Noah's CP2. One of my favorite non-main methods.

Next: R' B' L2 F2 U2 R D2 R' B2 D2 L U2 L B D L U F' L2 F2
 
Renslay said:
 Twizzle link 
 Setup 
L U2 F2 L' B2 L2 U2 B2 R' D2 F2 L B' F L' B' R F2 D' U R2
 Moves 
y z'
b R2 b' U' B2 U' R B' // FB
U' r U R' U' F' U' F // CP
r' U r R U2 r U r' // EO
U' M2 U r2 // 223
R' U R U' R2 U R' U' R U2 R' U R // F2L
U' R' U2 R2 U R U R U' R' U' R2 U R U2 // 2GLL


I did a CEOR, a.k.a. Noah's CP2. One of my favorite non-main methods.

Next: R' B' L2 F2 U2 R D2 R' B2 D2 L U2 L B D L U F' L2 F2
Click to expand...
 Twizzle link 
 Setup 
R' B' L2 F2 U2 R D2 R' B2 D2 L U2 L B D L U F' L2 F2
 Moves 
z2 // Inspection
F' B' R2 D2 R' D // Cross
U' F U2 F' U' L U L' // 1st Pair
F' U F U2 B U B' // 2nd Pair
D R' F R F' D2 y' R U R' U F' U' F D // Psuedo-Pair
y2 Fw R U R' U' Fw' R' U2 R U R' U R // OLL
y L' U' L F L' U' L U L F' L2 U L U'

Next
 
Aurora III, 48 moves

 Twizzle link 
 Setup 
L U2 B R2 B2 L2 U2 B' D2 B U' L B' U2 L' B2 F2 U
 Moves 
z2 // inspection
S U2 S' R U R' U' R2 L U' L' U2 r U2 r' // 223 (15/48)
U' R U R U R' U2 R F R' F' // dfR square + pair skip (11/48)
f R' F' R f' U2 F R //rf2g (8/48)
U R' U2 R U R' U R2 U R' U R U2 R' // 2gll (14/48)


Next: L' D2 B R U2 L U F2 D2 B2 R' L2 U2 B2 R B2 D2 F2 L' B R2
 
CrossPetrus said:
Next: L' D2 B R U2 L U F2 D2 B2 R' L2 U2 B2 R B2 D2 F2 L' B R2
Click to expand...

Roux!

 Twizzle link 
 Setup 
L' D2 B R U2 L U F2 D2 B2 R' L2 U2 B2 R B2 D2 F2 L' B R2
 Moves 
y' x
F' E B2 U2 R' U F' // FB
U2 R' U2 R U' R' U' R' U' M U' r // SB
U' l U R' D R U' R U' R2' D' R U l' // CMLL
U' M' U' M' U' M' U M2 U' M' U2 M2 U2 // LSE


Next: L2 B' D' L B' R' L D U2 F2 L F2 R D2 R' U2 D2 F2 R' F' R
 
Renslay said:
Next: L2 B' D' L B' R' L D U2 F2 L F2 R D2 R' U2 D2 F2 R' F' R
Click to expand...
 Twizzle link 
 Setup 
L2 B' D' L B' R' L D U2 F2 L F2 R D2 R' U2 D2 F2 R' F' R
 Moves 
// ZZ-VH
F D M U' M' D2 F2 (U D') F2 // EO Xcross (10)
U' L U L' R U' R' // dFR (7/17)
U2' L R' U R // dBR (5/22)
U L' U2' L U L' //dBL (6/28)
U2' R' F2 R U2' R U2' R' F2 U' R U' R' // COLL (13/41)
L2 U' S' L2' S L2 U L2' // EPLL (8/49)


NEXT: D L' D2 L2 U2 B2 L' U2 B2 L' B2 U2 B2 U' F L B F L R B
 
tsmosher said:
 Twizzle link 
 Setup 
L2 B' D' L B' R' L D U2 F2 L F2 R D2 R' U2 D2 F2 R' F' R
 Moves 
// ZZ-VH
F D M U' M' D2 F2 (U D') F2 // EO Xcross (10)
U' L U L' R U' R' // dFR (7/17)
U2' L R' U R // dBR (5/22)
U L' U2' L U L' //dBL (6/28)
U2' R' F2 R U2' R U2' R' F2 U' R U' R' // COLL (13/41)
L2 U' S' L2' S L2 U L2' // EPLL (8/49)


NEXT: D L' D2 L2 U2 B2 L' U2 B2 L' B2 U2 B2 U' F L B F L R B
Click to expand...
Aurora III, 48 moves

 Twizzle link 
 Setup 
D L' D2 L2 U2 B2 L' U2 B2 L' B2 U2 B2 U' F L B F L R B
 Moves 
y2 // inspection 
D' R' U' M F U M2 U2 B U' r U r' U2 r' //223 (15/48)
R2 U R' S' U' S U R' U2 R U R' // rb (12/48)
U F' U2 F2 R' F' R U R //rf2g (9/48)
U' R U2 R2 U2 R2 U R2 U R2 U' R' // 2gll (12/48)


Next: B' L2 B2 U2 B U2 R2 B U2 F' L2 R B2 L' D F2 R2 B' R2 F
 
CrossPetrus said:
Next: B' L2 B2 U2 B U2 R2 B U2 F' L2 R B2 L' D F2 R2 B' R2 F
Click to expand...

Roux speedsolve.

 Twizzle link 
 Setup 
B' L2 B2 U2 B U2 R2 B U2 F' L2 R B2 L' D F2 R2 B' R2 F
 Moves 
y z
R B' r2 D U R B' // FB
R' U' M r' U r U R U2 r U2 r U' R' // SB
U' U L' U' L U L F' L' F // CMLL
M' U' M U2 M U' M' U' M U2 M' U' M' U2 M2 U2 M // CMLL


Next: R2 F2 U2 D' L F L F2 U' B2 D2 R D2 L F2 R2 U2 D2 R2
 
Renslay said:
Next: R2 F2 U2 D' L F L F2 U' B2 D2 R D2 L F2 R2 U2 D2 R2
Click to expand...

An easy Roux solve.

 Twizzle link 
 Setup 
R2 F2 U2 D' L F L F2 U' B2 D2 R D2 L F2 R2 U2 D2 R2
 Moves 
x y'
E r U' b R2 U' B2 // FB
R' r2 U R' U2 r2 U M' U2 R' U r // SB
U F R U R' U' R U R' U' F' // CMLL
U2 M U' M' U' M2 U M' U2 M U2 // LSE


Next: L2 F' L2 D2 F L2 F' R2 U2 L2 B L' D' F' R B D' B2 L U2
 
Renslay said:
An easy Roux solve.

 Twizzle link 
 Setup 
R2 F2 U2 D' L F L F2 U' B2 D2 R D2 L F2 R2 U2 D2 R2
 Moves 
x y'
E r U' b R2 U' B2 // FB
R' r2 U R' U2 r2 U M' U2 R' U r // SB
U F R U R' U' R U R' U' F' // CMLL
U2 M U' M' U' M2 U M' U2 M U2 // LSE


Next: L2 F' L2 D2 F L2 F' R2 U2 L2 B L' D' F' R B D' B2 L U2
Click to expand...
This one is actually good, 57 OB, 50 RB, and a 19-move F2S+LEFI
 Twizzle link 
 Setup 
L2 F' L2 D2 F L2 F' R2 U2 L2 B L' D' F' R B D' B2 L U2
 Moves 
z2 y // Inspection
D' U' F' U F D y2 x U Rw' U' R U M' U Rw' U2 R U R' y // F2S+LEFI
R S R S' // EO
R2 U' R' U S U2 S' // L2DE+NFL
R' U R U' // Numann Second Look
R' U R' D' R U2 R' D R2 // Numann Third Look
y R2 U S' U2 S U R2 U' // PLL

Next: U2 L2 U F2 U B2 U R2 U R2 L' F2 D2 B R2 D2 U2 B' R U
 
acrystal said:
This one is actually good, 57 OB, 50 RB, and a 19-move F2S+LEFI
 Twizzle link 
 Setup 
L2 F' L2 D2 F L2 F' R2 U2 L2 B L' D' F' R B D' B2 L U2
 Moves 
z2 y // Inspection
D' U' F' U F D y2 x U Rw' U' R U M' U Rw' U2 R U R' y // F2S+LEFI
R S R S' // EO
R2 U' R' U S U2 S' // L2DE+NFL
R' U R U' // Numann Second Look
R' U R' D' R U2 R' D R2 // Numann Third Look
y R2 U S' U2 S U R2 U' // PLL

Next: U2 L2 U F2 U B2 U R2 U R2 L' F2 D2 B R2 D2 U2 B' R U
Click to expand...
Aurora III, 44 moves

 Twizzle link 
 Setup 
U2 L2 U F2 U B2 U R2 U R2 L' F2 D2 B R2 D2 U2 B' R U
 Moves 
y2 //inspection
F2 D' B L' B2 R U' M' B' r2 U r //223 (12/44)
R2 U2 R U' R' U R2 u R U R' u' F'
U' F // rb (15/44)
U2 f R' F' R f' U2 F R //rf2g (9/44)
R2 U' S' U2 S U' R2 U2 //2gll (7/44)


Next: L2 F' U2 R2 B2 R2 F2 D2 L F2 L B2 R F2 U' F' D2 R' B F L
 
You must log in or register to reply here.

Similar threads

M
The One Move 3x3x3 example solve!
20 21 22
Replies
425
Views
47,186
Renslay
Renslay
D
Feliks 3x3x3 example solves
2
Replies
21
Views
6,909
Deleted member 36445
D
SpeedSolver101
[Unofficial] 3x3x3 Example Solve + Timed Solve
Replies
0
Views
1,791
SpeedSolver101
SpeedSolver101
JF1zl3
[Unofficial] 4 HD Quality Example 3x3x3 Solves
Replies
2
Views
1,392
JF1zl3
JF1zl3
N
  • Locked
[Unofficial] Example solve 3x3 Begginers method
Replies
2
Views
1,474
PandaCuber
PandaCuber
Back
Top