God's number table

[Piotr Grochowski]

https://pastebin.com/JUfcdSjv
If you give me better bounds, the table will be updated.

Metric introduction:

2x2, Kilominx, Megaminx:
QTM (Quarter Turn Metric) - "quarter" turn of a face is a turn.
HTM (Half Turn Metric) - any turn of a face is a turn.

3x3:
QTM (Quarter Turn Metric) - quarter turn of one face is a turn.
QSTM (Quarter Slice Turn Metric) - quarter turn of one slice is a turn.
HTM (Half Turn Metric) - any turn of one face is a turn.
STM (Slice Turn Metric) - any turn of one slice is a turn.

4x4-9x9:
QWTM (Quarter Wide Turn Metric) - quarter turn of an outer block is a turn.
QSTM (Quarter Slice Turn Metric) - quarter turn of one slice is a turn.
QBTM (Quarter Block Turn Metric) - quarter turn of a block of layers is a turn.
WTM (Wide Turn Metric) - any turn of an outer block is a turn.
STM (Slice Turn Metric) - any turn of one slice is a turn.
BTM (Block Turn Metric) - any turn of a block of layers is a turn.

Pyraminx:
WTM (Wide Turn Metric) - a turn of an outer block (either from face or tip) is a turn.
STM (Slice Turn Metric) - a turn of a slice is a turn; superset of WTM as a single face rotation is equivalent to double tip rotation, and vice-versa.

Jing's Pyraminx:
TM (Turn Metric) - a turn is a turn. There are no additional turn metrics, because there are only 2 layers, and "half" turns are not needed on faces with 3 orientations.

Master Pyraminx:
WTM (Wide Turn Metric) - a turn of an outer block (either from face or tip) is a turn.
STM (Slice Turn Metric) - a turn of one slice is a turn.
BTM (Block Turn Metric) - a turn of a block of layers is a turn.

 

[xyzzy]

If you give me better bounds, the table will be updated.

What's your contribution to the table? Do you just want other people to fill it in for you?

 

[Piotr Grochowski]

What's your contribution to the table? Do you just want other people to fill it in for you?

This is a table for public to look at God's numbers. People can inform better lower or upper bounds found and I will update it then. Most people, including me, don't have the computational applications to calculate better bounds.

 

[Dancing Jules]

... better lower or upper bounds

There's not a single number in your table. You could at least write in the HTM 20 for 3x3. Everybody knows that.

 

[xyzzy]

There's not a single number in your table. You could at least write in the HTM 20 for 3x3. Everybody knows that.

Just to be fair, the table does have the current known bounds for 2×2×2 and 3×3×3. It just doesn't have anything else.

 

[AlphaSheep]

https://pastebin.com/JUfcdSjv
If you give me better bounds, the table will be updated

I wonder if maybe https://hackmd.io would be better for this kind of thing.

 

[Piotr Grochowski]

The table has been updated with internet data.

 

[Dancing Jules]

Just to be fair, the table does have the current known bounds for 2×2×2 and 3×3×3.

Ah, sorry. I did not see the link at first.

 

[Piotr Grochowski]

Now updated with the 135 5x5 upper bound number!

 

[ananasclassic]

The 4x4x4 WTM/OBTM upper bound can be updated from 55 to 54.

The proof uses a new exact 18-move bound for phases 1+2, combined with the published 16- and 20-move bounds.

Details: https://www.speedsolving.com/threads/4x4x4-obtm-wtm-upper-bound-improved-from-55-to-54.97372
Artifact: https://github.com/AnanasClassic/4x4x4-obtm-54-research