God's number for selected 3x3x3 stages

[bcube]

Hi,

Thistlethwaite's algorithm can be schematically expressed as follows:

Scrambled cube → EO → DR → HTR → Solved cube

I am wondering whether God's number is known for these 3x3x3 stages in HTM when all 18 possible moves are allowed?

• EO → HTR = ?
• DR → HTR = ? (upper bound: 13)

God's number in HTM when all 18 possible moves are allowed is known for:

• Scrambled → EO = 7 (distance distribution)
• Scrambled → DR = 12 (distance distribution)
• Scrambled → HTR = 16 (distance distribution)
• Scrambled → Solved = 20 (proof)
• EO → DR = 10 (distance distribution)
• EO → Solved = 20 (example)
• DR → Solved = 18 (distance distribution on page 4)
• HTR → Solved = 13 (distance distribution)

 

[xyzzy]

EO to DR: still 10 moves
Distribution: https://www.speedsolving.com/threads/probability-thread.20384/post-1490774

DR to solved: still 18 moves
Distribution: https://arxiv.org/abs/0803.3435 page 4

EO to solved: still 20 moves
I don't think distribution has been computed; some of the pure-corner-twist scrambles are 20 optimal iirc.

 

[xyzzy]

some of the pure-corner-twist scrambles are 20 optimal iirc.

I remembered wrongly; there is this example which is 8-twist (seven cw, one ccw) composed with 4-spot:

 Twizzle link 

U F R2 D' F' L2 U F' B' U F' B' U L2 B' D' F R2 U F'

(From Chong Wen on the FMC Discord who in turn got it from CF.)

 

[Caleb Valenzuela]

Hi,

Thistlethwaite's algorithm can be schematically expressed as follows:

Scrambled cube → EO → DR → HTR → Solved cube

I am wondering whether God's number is known for these 3x3x3 stages in HTM when all 18 possible moves are allowed?

• EO → HTR = ?
• DR → HTR = ? (upper bound: 13)

God's number in HTM when all 18 possible moves are allowed is known for:

• Scrambled → EO = 7 (mention)
• Scrambled → DR = 12 (distance distribution)
• Scrambled → HTR = 16 (distance distribution)
• Scrambled → Solved = 20 (proof)
• EO → DR = 10 (distance distribution)
• EO → Solved = 20 (mention)
• DR → Solved = 18 (distance distribution on page 4)
• HTR → Solved = 13 (distance distribution)

is this how FMC works??

 

[bcube]

is this how FMC works??

Yes, competitors are mimicking the steps from Thistlethwaite's algorithm in FMC.

 

[UMichSpeedCubist]

DR to HTR is 13.

 

[UMichSpeedCubist]

For EO to HTR, I was only able to get a partial table. The number of cases really explodes.

 

[bcube]

DR to HTR is 13.
View attachment 46048

Hmmm, something is wrong. Could you please elaborate?

Scrambled → EO: 2,048 cases
EO → DR: 1,082,565 cases
DR → HTR: 29,400 cases
HTR → Solved: 663,552 cases

 

[UMichSpeedCubist]

Hmmm, something is wrong. Could you please elaborate?

Scrambled → EO: 2,048 cases
EO → DR: 1,082,565 cases
DR → HTR: 29,400 cases
HTR → Solved: 663,552 cases

What is the problem? Is my total case-count wrong? This is solving HTR with DR completed and not breaking the DR, i.e. staying within the subgroup.

 

[UMichSpeedCubist]

I found some mistakes in my computation. I reran it and found gods number 9 with only 4900 cases. But this also doesn't match the number of cases you put forth, so Idk if I did it right this time.

 

[bcube]

I found some mistakes in my computation. I reran it and found gods number 9 with only 4900 cases. But this also doesn't match the number of cases you put forth, so Idk if I did it right this time.

Easy check: 2,048 * 1,082,565 * X * 663,552 = 43,252,003,274,489,856,000

This is solving HTR with DR completed and not breaking the DR, i.e. staying within the subgroup.

Perhaps you missed the point. The point is using the <U, D, R, L, F, B> move set in all stages (see links in the first post).

 

[UMichSpeedCubist]

Omg, I completely missed the part "when all 18 possible moves are allowed".

I agree with the numbers 2048, 1082565, and 663552 as my tool gives those same values. And your equation makes sense. So I need to figure out where I went wrong.

 

[bcube]

Maybe this could help.