One-Answer Puzzle Theory Question Thread

[Discomantis]

Hello everyone. I was wondering how many known 2x2 positions there are that would require 10 moves in HTM and 14 moves in QTM. Sorry if there has already been something discussed about this, but I have been searching for the answer to this for a while, but I couldn't find it.

 

[Ben Whitmore]

Mini Cube, the 2x2x2 Rubik's Cube

www.jaapsch.net

 

[Bruce MacKenzie]

Here are the numbers

​	FTM​	QTM​
0​	1​	1​
1​	9​	6​
2​	54​	27​
3​	321​	120​
4​	1,847​	534​
5​	9,992​	2,256​
6​	50,136​	8,969​
7​	227,536​	33,058​
8​	870,072​	114,149​
9​	1,887,748​	360,508​
10​	623,800​	930,588​
11​	2,644​	1,350,852​
12​	​	782,536​
13​	​	90,280​
14​	​	276​

 

[Bruce MacKenzie]

what is the god's number for one side on a 3x3 cube? i mean side, not layer

Turns out I have a optimal 3x3 solver that uses solving one face for pruning. The answer is 12f. Here are the numbers for the pruning table (the table is symmetry reduced so the actual numbers are aprox 8x these).

Prune Table
Subgroup with fixed cubies:
UF UR UB UL UFR URB UBL ULF
Corner Move Table(C4v reduced): 17214
Edge Move Table: 190080

Cosets at Depth
Depth: 0 count: 1
Depth: 1 count: 4
Depth: 2 count: 28
Depth: 3 count: 347
Depth: 4 count: 4,245
Depth: 5 count: 50,232
Depth: 6 count: 585,973
Depth: 7 count: 6,574,538
Depth: 8 count: 66,874,490
Depth: 9 count: 520,466,809
Depth: 10 count: 1,834,132,108
Depth: 11 count: 840,988,604
Depth: 12 count: 2,359,741
Total: 3,272,037,120
Pruning table complete

 

[Discomantis]

What is god's number for solving a 3x3 if you solve it using only five gen moves (because the 3x3 can be solved without turning one side from any position.)

 

[Bruce MacKenzie]

What is god's number for solving a 3x3 if you solve it using only five gen moves (because the 3x3 can be solved without turning one side from any position.)

I would be tremendously surprised if that were known.

 

[Thom S.]

I would be tremendously surprised if that were known.

On my way to hopelessly contact google again.

 

[Silky]

What is God's number to get to DR? And likewise to get from DR to HTR?

 

[Bruce MacKenzie]

What is God's number to get to DR? And likewise to get from DR to HTR?

See https://www.speedsolving.com/wiki/index.php/Domino_Reduction

 

[Silky]

See https://www.speedsolving.com/wiki/index.php/Domino_Reduction

I read over this articles. For DR's God's number the wording is a bit vague. Wasn't sure if it was saying it took at most 12 moves to get TO domino reduction or it took 12 moves FROM domino reduction to get to a solved state. Turns out it was the former.

 

[Filipe Teixeira]

How many cases will be if the last layer is phased, corners are oriented and any 2 or more ll edges are oriented?

 

[PapaSmurf]

It's approximately the number of two flip COALL/ELLCP/CPELL/PLLEF/EFPLL/anti-ZBLL cases divided by 3. I currently don't have the number of COALL cases.