# 1x2x2 Block Move-count



## rubiksfriend (Jul 9, 2008)

Finally, a thread from me not about Waterman! Ok, Lars V did a computation and found that it takes 8 moves max to make the cross. How many moves max does it take to make a 1x2x2 block (sub-step of 1st step of Roux)? How many for a 1x2x3 block?


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## waffle=ijm (Jul 9, 2008)

It takes me about 4 moves to get a 1x2x2 block if the pieces are easy to get to. if not (which is unlikely because you have the entire cube to work from) up to 6 moves.the entire 1x2x3 block takes me about 8-10 moves in general. *HOWEVER* I can't do a low move count while speedsolving because I panic and go up to 12-14 moves to get 1x2x3 block


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## rubiksfriend (Jul 9, 2008)

I know what you mean! Right now, I'm working on building a 1x2x2 block, then pairing up the corner and edge, aligning the edge in the slot, or aligning the corner in the slot, solving the missing piece, then inserting. I'm sure there are other ways though (1x1x2 block, solving opp. edges, inserting).


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## waffle=ijm (Jul 9, 2008)

Yeah that's like my approach to it but its slowing me down too much. I think the 1x1x2 blocks won't be as good as the 1x2x2 block. I can't seem to find easy cases to place edges in. I'm thinking about fixing an edge and then simultaneously making two pairs and attach to the edge. Its possible with the first 1x2x3 block but the amount of moves would go up


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## MistArts (Jul 9, 2008)

I think 4. I'm not sure becuase in FMC, I write down the explanation as a 2x2x2 block(I make a 1x2x2 block before it) and is usally 4-6 moves for the 2x2x2 blcok,


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## AvGalen (Jul 9, 2008)

I guesstimate 3.0000001 for 1x2x2 and 4.99999999 for 1x2x3. This is also based on my FMC experience where 2x2x2 takes me 5 moves and 2x2x3 takes me 8 moves on average (allowing for premoves)


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## MistArts (Jul 9, 2008)

AvGalen said:


> I guesstimate 3.0000001 for 1x2x2 and 4.99999999 for 1x2x3. This is also based on my FMC experience where 2x2x2 takes me 5 moves and 2x2x3 takes me 8 moves on average (allowing for premoves)



Hey, I know this is off-topic but what are premoves and what do they do?


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## AvGalen (Jul 9, 2008)

I explain premoves in the Fewest Moves tutorial 
Sometimes they are easy to see and understand
Sometimes they are more difficult to see and understand (but they turn a 4th pair from 7/8 moves into a "2 premoves only")


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## brunson (Jul 9, 2008)

I believe Johannes91 did a brute force calculation of all scramble -> 1x2x2 and 1x2x2 -> 1x2x3 solutions for a web application. He could tell us the max length of both.


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## Johannes91 (Jul 9, 2008)

brunson said:


> I believe Johannes91 did a brute force calculation of all scramble -> 1x2x2 and 1x2x2 -> 1x2x3 solutions for a web application. He could tell us the max length of both.


Nope, I did the Petrus steps which are 2x2x2 and 2x2x2 -> 2x2x3 (move counts for those can be found here and for direct 2x2x3 here).

There are only 11520 cases for 1x2x2, so it's trivial to compute. I'll probably do it unless someone else does it first. Maybe also 1x2x3.

Edit: Hmm, seems like I misread and the OP is looking for the move counts with color neutrality. Those are less trivial to find.

Edit 2: Where did I get that 11520 from?! It's 12672.


```
Creating pruning table: 1x2x2
Depth: 0, Positions found: 1
Depth: 1, Positions found: 10
Depth: 2, Positions found: 88
Depth: 3, Positions found: 678
Depth: 4, Positions found: 3600
Depth: 5, Positions found: 10123
Depth: 6, Positions found: 12648
Depth: 7, Positions found: 12672
Done.
```

Here are solutions to the positions at depth 7, 1x2x2 is at UFR:

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

I didn't consider 1x2x2 solved if it doesn't match with the F and R centers. This is probably not how Roux people see it.


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## Johannes91 (Jul 10, 2008)

```
Creating pruning table: 1x2x3
Depth: 0, Positions found: 1
Depth: 1, Positions found: 13
Depth: 2, Positions found: 145
Depth: 3, Positions found: 1551
Depth: 4, Positions found: 15650
Depth: 5, Positions found: 137929
Depth: 6, Positions found: 935074
Depth: 7, Positions found: 3573712
Depth: 8, Positions found: 5288780
Depth: 9, Positions found: 5322240
Done.
```
Again, I considered the centers important. But there are so many positions at depth 9 that I'd guess it'd be the worst case anyway.


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## MistArts (Jul 10, 2008)

Hey, is all those with color neutrality?


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## Johannes91 (Jul 10, 2008)

MistArts said:


> Hey, is all those with color neutrality?


Nope, fixed colors (I thought it's obvious because the numbers are so small). I don't know how to get accurate numbers with color neutrality in a reasonable time. For cross it's doable because you only need to care about edges.


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## rubiksfriend (Jul 19, 2008)

Looks like I have work to do. XO Thanks for the info, Johannes.


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## hawkmp4 (Jul 22, 2008)

Sorry for reviving an old topic, but Johannes, how exactly do you do these calculations? Like, what program/s do you use?


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