The 3x3x3 Example Solve Thread

acrystal · Jun 1, 2026

PhanPhuocan said:
method: APB
Solve:
x2 // orientation
F' U R' D L2 F R2 B R' B' U' B // 2x2x3
R' U B U' B' //Pair
U2 S' U S// EO
R U F' R U R' U' R' F R U R' //LXS
U' l U2 l' U2 R' U2 R B2 U R' U R //ZBLL
Next: R B2 D2 L' U2 F2 R' U2 L' D2 F2 R U L' F D2 R' F L F2 R'

Using Advanced Orcora Petrus

alg.cubing.net

Next Scramble: R U' F2 L2 D L2 R2 B2 L2 D' U' R2 U' B' F' U' R' B2 R2 U' R'

Renslay · Jun 2, 2026

acrystal said:
Next Scramble: R U' F2 L2 D L2 R2 B2 L2 D' U' R2 U' B' F' U' R' B2 R2 U' R'

Twizzle link

Setup

R U' F2 L2 D L2 R2 B2 L2 D' U' R2 U' B' F' U' R' B2 R2 U' R'

Moves

// Roux speedsolve, yellow left, red bottom
y' z2
r' U' R' r2 u' R' F2 U F' // FB 9
r U2 r' U' R U' R2 r' U M' U R' U2 R // SB 14
F R' F' R U R U' R' // CMLL 8
M' U' M' U2 M' U M' // EO 7
U2 M2 U' // UL/UR 3
M2 U2 M U2 M' // Mperm 5

Next:
R2 B' R2 B' D2 B2 U2 B2 R2 B' U R' D' R' B' D2 B' F2 D

abunickabhi · Jun 5, 2026

Renslay said:

z2 y
//e udal icmt spob
//c vmjg apau qc

M D S L S' D M' D' L' D' //UF-DB-DF-UL-BL
R2 E U S' U2 R S2 R' S' u R2 //UF-FL-UR-BR-DL
[S U L' : [E', L2]] [U' : [L E' L', U2]]

[R': [F', R D' R' D]]
[R B R' U D' : [R D R', U2]]
[D : [R' D R, U']]
[R D' R' : [R' D R, U']]
[D : [R D' R', U']]

recon

Next: R' B' F2 R2 U' F2 U L2 U R2 U R2 D' F' D' R B L R F' R2

Renslay · Jun 5, 2026

abunickabhi said:
Next: R' B' F2 R2 U' F2 U L2 U R2 U R2 D' F' D' R B L R F' R2

Twizzle link

Setup

R' B' F2 R2 U' F2 U L2 U R2 U R2 D' F' D' R B L R F' R2

Moves

// Roux speedsolve, white left, red bottom
z'
R' U2 L D' U2 R U' R r B' // FB 10
M U2 R' U' R' U' r' U R U' r2 R U r // SB 14
U' R2 D R' U2 R D' R' U2 R' // CMLL 10
M U M' U2 M' U M' U' M' U2 M' U // LSE 12

Next: D' L F2 U2 F' R2 L B R U2 F2 D' B2 U2 R2 F2 D2 R2 F2 U D

carcass · Jun 17, 2026

Renslay said:
D' L F2 U2 F' R2 L B R U2 F2 D' B2 U2 R2 F2 D2 R2 F2 U D

42 STM

y' x
U B U' r' U' R' F
M' U R U r
F' U2 F
R' U M' U' R
U2 f R' f' M U2 M'
y' R' U2 R U R' U R U' R' U' F' U F R U2 (1LLL alg from the internet lol)

next scramble: R2 U2 B2 U' F2 U' B2 R2 U2 L2 U2 F' D L' B L' B F2 U2 B R'

Renslay · Jun 17, 2026

Human Thistlethwaite Algorithm, because why not, we don't have enough of these.

60 HTM, 57 STM, not bad!

Twizzle link

Setup

R2 U2 B2 U' F2 U' B2 R2 U2 L2 U2 F' D L' B L' B F2 U2 B R'

Moves

// Human Thistlethwaite Algorithm
z
B R L D F // <U,D,L,R,F2,B2>
R U D' L // <U,D,L2,R2,F2,B2> edges
U' L' U' L U' L' U2 L B2 U' L' U' L U' L' U2 L // <U,D,L2,R2,F2,B2> corners
D L2 D R2 U R' F R' B2 R F' R // <U2,D2,L2,R2,F2,B2> corners
L2 U2 F2 U' M2 U' // <U2,D2,L2,R2,F2,B2> edges
F2 U2 R2 // <> corners
D2 R2 B2 R2 B2 R2 B2 S2 D2 S2 // <> edges

Next: B2 R2 F2 D2 U' B2 R2 D R2 D L2 B2 F R' F' L' B' D2 R2 B D

acrystal · Jun 19, 2026

Renslay said:
Human Thistlethwaite Algorithm, because why not, we don't have enough of these.

60 HTM, 57 STM, not bad!

Twizzle link
Setup
R2 U2 B2 U' F2 U' B2 R2 U2 L2 U2 F' D L' B L' B F2 U2 B R'
Moves
// Human Thistlethwaite Algorithm z B R L D F // <U,D,L,R,F2,B2> R U D' L // <U,D,L2,R2,F2,B2> edges U' L' U' L U' L' U2 L B2 U' L' U' L U' L' U2 L // <U,D,L2,R2,F2,B2> corners D L2 D R2 U R' F R' B2 R F' R // <U2,D2,L2,R2,F2,B2> corners L2 U2 F2 U' M2 U' // <U2,D2,L2,R2,F2,B2> edges F2 U2 R2 // <> corners D2 R2 B2 R2 B2 R2 B2 S2 D2 S2 // <> edges

Next: B2 R2 F2 D2 U' B2 R2 D R2 D L2 B2 F R' F' L' B' D2 R2 B D

Advanced Orcora Petrus

Twizzle link

Setup

B2 R2 F2 D2 U' B2 R2 D R2 D L2 B2 F R' F' L' B' D2 R2 B D

Moves

z2 // Inspection
U D' R B' L B F' U F' R U2 R' y2 // F2S+LEFI
U' R' S' U S B U B' // EO
U' S' R2 S R2 // L2DE
R U2 R' U' R U R2 U2 R // Numann First Look
R U' R' U2 R U2 R' U2 // Numann Second Look
R U' R' U' R U' R' // Numann Third Look
R2 U' R U' R U R' U R2 D' U R U' R' D U' // PLL

Next: B R' D' L' B' U' R D' B2 L F U2 R2 L2 D2 R2 B' D2 F D2

Renslay · Jun 22, 2026

acrystal said:
Next: B R' D' L' B' U' R D' B2 L F U2 R2 L2 D2 R2 B' D2 F D2

Twizzle link

Setup

B R' D' L' B' U' R D' B2 L F U2 R2 L2 D2 R2 B' D2 F D2

Moves

y2 z'
F R2 r F R2 B r2 B // FB 8
U2 R U' r U2 R' U' R U R U' R U' R' U R // SB16
R' U' R U' R' U R U' R' U2 R // CMLL 11
U M U M' U2 M' U M' U M' U2 M' U' // LSE 13

Next: D2 R2 D2 B2 L2 U2 B R2 F2 R' U' F L' R F' R F U

acrystal · Jun 25, 2026

Renslay said:
Twizzle link
Setup
B R' D' L' B' U' R D' B2 L F U2 R2 L2 D2 R2 B' D2 F D2
Moves
y2 z' F R2 r F R2 B r2 B // FB 8 U2 R U' r U2 R' U' R U R U' R U' R' U R // SB16 R' U' R U' R' U R U' R' U2 R // CMLL 11 U M U M' U2 M' U M' U M' U2 M' U' // LSE 13

Next: D2 R2 D2 B2 L2 U2 B R2 F2 R' U' F L' R F' R F U

Twizzle link

Setup

D2 R2 D2 B2 L2 U2 B R2 F2 R' U' F L' R F' R F U

Moves

z2 D2 F' D2 Rw U Rw' B L' R2 U R U' L2 y' U' S' U S2 U2 S' U R U' R' U' R2 U' R' U' R' U L U' R2 U R' U2 L' U2 L F' L' U' L U L F L2 U2 // Cancelled 7 moves in OBT Metric


//   z2 // Inspection
//   D2 F' D2 Rw U Rw' B L' R2 U R U' L2 y' // F2S+LEFI
//   U' S' U S // EO
//   S U2 S' R // L2DE
//   R' U R U' R' U' R // Numann First Look
//   R U' R' U' // Numann Second Look
//    R' U L U' R2 U R' L' // Numann Third Look
//    L U2 L' U2 L F' L' U' L U L F L2 U2 //PLL

Next: B' L D L' D' U2 R B U B2 U' R' F2 U L2 R' D R2 D B2 U F2 U B' R

Renslay · Jun 26, 2026

acrystal said:
Next: B' L D L' D' U2 R B U B2 U' R' F2 U L2 R' D R2 D B2 U F2 U B' R

Twizzle link

Setup

B' L D L' D' U2 R B U B2 U' R' F2 U L2 R' D R2 D B2 U F2 U B' R

Moves

z' x
R2 F2 B2 U2 B U' B // FB
R U' R2 U' r' U' M2 U r' U2 R' U r // SB
U F R U R' U' F' // CMLL
M U' M' U2 M' U M' // EO
U2 M' U2 M' U M2 U // ULUR
M U2 M U2 M2 // L3E

Next: D2 L2 D U2 R2 U' L2 U' L2 B2 U2 B' D' R' F' U2 B R' D2 R

acrystal · Jun 26, 2026

Renslay said:
Twizzle link
Setup
B' L D L' D' U2 R B U B2 U' R' F2 U L2 R' D R2 D B2 U F2 U B' R
Moves
z' x R2 F2 B2 U2 B U' B // FB R U' R2 U' r' U' M2 U r' U2 R' U r // SB U F R U R' U' F' // CMLL M U' M' U2 M' U M' // EO U2 M' U2 M' U M2 U // ULUR M U2 M U2 M2 // L3E

Next: D2 L2 D U2 R2 U' L2 U' L2 B2 U2 B' D' R' F' U2 B R' D2 R

Twizzle link

Setup

D2 L2 D U2 R2 U' L2 U' L2 B2 U2 B' D' R' F' U2 B R' D2 R

Moves

z2 // Inspection
F2 R' F' B2 D U2 R U' R' U' B U2 B' D' y // F2S+LEFI
R2 F R F' // EO
R2 U' S U2 S' // L2DE
D U' R' U R U' R' U R D' // Numann First Look
R' U R U' // Numann Second Look
R U' L' U R2 U' R L // Numann Third Look
y2 L' U' L F L' U' L U L F' L2 U L U // PLL

Next: D U' F' U2 F U' L' B2 D2 B2 L B L F D F2 R' D F2 R2 U2 D' L' B2 D2

Renslay · Jun 29, 2026

acrystal said:
Next: D U' F' U2 F U' L' B2 D2 B2 L B L F D F2 R' D F2 R2 U2 D' L' B2 D2

Twizzle link

Setup

D U' F' U2 F U' L' B2 D2 B2 L B L F D F2 R' D F2 R2 U2 D' L' B2 D2

Moves

// Roux solve, yellow left, red bottom
y' z
R U R r D R' U R' F // FB
r2 R U' M2 U R' U' M U' R2 r U' R // SB
U' R' D R U' R U' R' U R' D' R // CMLL
M' U M U' M' U' M' U M2 U M U2 M U2 M2 // LSE

Next: U L' B' D2 F L2 B R2 B2 F' D2 F L B D' B' U' R U

acrystal · Jul 3, 2026

Renslay said:

EO Skip, not bad

Twizzle link

Setup

U L' B' D2 F L2 B R2 B2 F' D2 F L B D' B' U' R U

Moves

z2 // " O z2! My z2! " - Walt Whitman
R D F L2 U' R D' Dw2 F Lw' U' Lw U Lw' U' L U M y
// F2S+LEFI
// EO Skip which is 1/64
S' R2 S U' S U2 S' // L2DE
R U' R' U2 R U R' // Numann First Look
R' U R // Numann Second Look
U2 R U R2 U R2 U2 R' // Numann Third Look - LWV
y' R U R' F' R U R' U' R' F R2 U' R' U // PLL

Next: R2 F2 D2 R2 B' L2 B F' R2 U2 F2 R F D' B R U2 B2 L R2 D

acrystal · Jul 5, 2026

acrystal said:

50 Move Solution w/ Orcora Petrus

Twizzle link

Setup

R2 F2 D2 R2 B' L2 B F' R2 U2 F2 R F D' B R U2 B2 L R2 D

Moves

z2 // " O z2! My z2! " - Walt Whitman
S' z L2 U' F R' L' U2 R' U' R U2 B U' B' y' // F2S+LEFI
S' U S B U B' // EO
S U2 S' U' R U' R U R U R' U' R' U2 R // 7 Moves cancelled in L2DE+N3L
y' R2 B2 R F R' B2 R F' R U // PLL

// S U2 S' U' R2 // L2DE
// R' U' R U R' U2 R // Numann First Look
// R' U2 R2 U R' U // Numann Second Look
// U2 R' U2 R // Numann Third Look

Next: U2 B R' D2 L U' D' R' B2 L2 U2 F L2 U2 L2 F2 L2 F' L

Renslay · Jul 6, 2026

acrystal said:
Next: U2 B R' D2 L U' D' R' B2 L2 U2 F L2 U2 L2 F2 L2 F' L

Human Thistlethwaite Algorithm - we need more of these!

Twizzle link

Setup

U2 B R' D2 L U' D' R' B2 L2 U2 F L2 U2 L2 F2 L2 F' L

Moves

// Human Thistlethwaite Algorithm
z
D' F U' D2 B // <U,D,L,R,F2,B2> 
U R D L // <U,D,L2,R2,F2,B2> edges
F2 U' R' D L2 D' R // <U,D,L2,R2,F2,B2> corners
F2 U R2 U R2 U' R2 U2 R' F R' B2 R F' R U' // <U2,D2,L2,R2,F2,B2> corners
R2 D L2 R2 U' // <U2,D2,L2,R2,F2,B2> edges
U2 B2 U2 B2 U2 B2 U2 R2 U2 R2 U2 B2 R L' D2 R' L // <>

Next: B2 R F2 U2 R2 F2 D2 F2 D R2 F2 D' B D2 U2 R D' B' U2

bcube · Jul 6, 2026

Renslay said:

I thought the text inside the brackets in your comments designates group generators which basically means "allowed move set" (you should start with <U,D,R,L,F,B>). If that's the case, your solution is *not valid* because you do not use allowed move set (e.g. when making corners half-turn solvable).

Renslay said:
Human Thistlethwaite Algorithm - we need more of these!

Agreed. But I prefer the 3-color cube method

Next scramble: L2 R2 B F2 R2 F' D2 L2 F' L2 D' L R2 D B U' F' L' D U

Renslay · Jul 7, 2026

bcube said:
I thought the text inside the brackets in your comments designates group generators which basically means "allowed move set" (you should start with <U,D,R,L,F,B>). If that's the case, your solution is *not valid* because you do not use allowed move set (e.g. when making corners half-turn solvable).

No. The text inside the brackets mean the cube is in that state where it can be solved using only those moves. For example this line:

z D' F U' D2 B // <U,D,L,R,F2,B2>

means that after performing z D' F U' D2 B, the cube is now in a state where it can be solved using only U, D, L, R, F2, and B2 moves (and their inverses).

Now just because it can, does not mean it must.

Similarly, if you're using a method that solves the F2L and brings the cube to a <R,U> state for the LL (also called 2GLL), that means you can finish the LL using only R and U moves... But you don't have to. See this for example:

This is a 2GLL case (a subset of ZBLL), yet the second algorithm does not use <R,U>. No one says that "no, you can't use that algorithm!"

Similarly, in the Human Thistlethwaite Algorithm, nothing forbids you to use algorithms that temporary breaks the state you brought the cube into. For example, in the last stage of <U2,D2,L2,R2,F2,B2>, you can use:
D2 F2 D2 R2 B2 R2 B2 R2 B2 D2 F2 D2
But why would do when this is the same but shorter and faster:
R' U2 R2 U2 R2 U2 R'

Twizzle link

Setup

D2 F2 D2 R2 B2 R2 B2 R2 B2 D2 F2 D2

Moves

R' U2 R2 U2 R2 U2 R'

bcube · Jul 7, 2026

Renslay said:
Now just because it can, does not mean it must.

Renslay said:
Similarly, in the Human Thistlethwaite Algorithm, nothing forbids you to use algorithms that temporary breaks the state you brought the cube into. For example, in the last stage of <U2,D2,L2,R2,F2,B2>, you can use:
D2 F2 D2 R2 B2 R2 B2 R2 B2 D2 F2 D2
But why would do when this is the same but shorter and faster:
R' U2 R2 U2 R2 U2 R'

I see what you are trying to say, however, I don´t see why you don´t write "<U2,D2,R2,L2,F2,B2>" as "<U,D,R,L,F,B>" then because:

1) all states generated by <U2,D2,R2,L2,F2,B2> can be generated by <U,D,R,L,F,B> as well, and
2) writting "<U,D,R,L,F,B>" instead of "<U2,D2,R2,L2,F2,B2>" is shorter and faster

Renslay · Jul 7, 2026

bcube said:
I see what you are trying to say, however, I don´t see why you don´t write "<U2,D2,R2,L2,F2,B2>" as "<U,D,R,L,F,B>" then because:

1) all states generated by <U2,D2,R2,L2,F2,B2> can be generated by <U,D,R,L,F,B> as well, and
2) writting "<U,D,R,L,F,B>" instead of "<U2,D2,R2,L2,F2,B2>" is shorter and faster

<U2,D2,R2,L2,F2,B2> and <U,D,R,L,F,B> are not the same. The <.> notation indicates a generator:

Generating set of a group - Wikipedia

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

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:

Thread 'The entire cube is 2-gen!'

Mar 10, 2010

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...

Renslay · Jul 7, 2026

bcube said:
Next scramble: L2 R2 B F2 R2 F' D2 L2 F' L2 D' L R2 D B U' F' L' D U

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

The 3x3x3 Example Solve Thread

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