I don't have a strong opinion on which image type to use. I would use option 4 for a standard 444 image.
Regarding parity permutation cases, I ran my recent program on them and came up with the following algorithms.
A few notes first:
- it searches in Single Slice Turn Metric...
My (4x4x4) solver gave a 19 moves solution: 2L2 D2 F 2L2 F' 2R F 2L2 F 2R' F2 2L D2 B2 U' 2R U B2 2L
EDIT: Well, I got a 17 moves solution: 2F2 R2 D2 U2 L2 U 2B L2 D2 2F' U2 R2 2F2 U2 2F' U 2F2
EDIT2: 15 moves solution: 2F2 U' R2 2B U2 2F L2 2F L2 2B' U2 R2 2F' U 2F2
Here are my solutions for BTM only. My solver cannot solve using double layer moves, so solutions are not optimised for OBTM metric.
1. F U 2R2 B2 L' B' L Fw' R2 Rw' 2U2 B' 2L' 2F2 2L2 2R' 2B' 2D' B' 2U2 B2 D2 (L2 R2) D2 2D Lw2 F' R2 B' 2B2 2L2 B' Lw2 D2 B2 L2 2F2 (37)
2. U 2F' 2D F D'...
Here are my solutions:
1. L' D2 2L2 U' F' U2 2D 2F2 L' 2R' 2U' F 2B 2D B2 2L' 2F2 R2 F B2 2U' F' B2 2D' F2 R2 2U2 L2 B 2D2 F2 U2 F 2R2 U2 2F2 2L2 U2 2L2 2F2 2L2 (41)
2. 2F' D F' 2F2 2U2 B2 R D F2 L' U' 2L' 2U F2 2D' 2L2 2F 2L' 2U2 2R2 U' B2 R2 2F2 2L' 2U2 D B2 U' 2L2 2B2 R2 D 2B2 U2 R2 2F2 2R2...
Wow, I've not been here for ages.
This is so nice to see a computer contest for 4x4x4 FMC. I will dig my code from the graves and see how it goes on the 5 scrambles. I remember it having an average solution of 40 moves, but it was designed for fast solutions (about 1 sec), I've no idea if it can...
Ok, but where is the limit ? How do you judge if the gap is big enough so that you only consider putting it back in that location ? You want to introduce the term 'reasonable' in the regulations ?
Vincent said that the task is to reassemble the puzzle, not to reassemble the puzzle while...
The problem here is that you require that the judge has enough knowledge to know that it is unambiguously solved. If you write the rule like you suggest, then a lot of judges would not be able to judge if it is solved or not.
If this case is too simple for you, consider the case where you remove...
Thank you, Bruce.
About your first point, I was trying to solve using hex-search (3 orientations + inverse), but I soon realized that because the centers do not form a group, you could not use the inverse position. This has already been fixed in my own repository...
Go to France
I'm a little late. I like this proposal. Here is an alternative without flipping the clock :
U4+ d3- R2- l3+ D1- u2- L6+ r5+ UL3+ UR4- DR6+ DL4+ A3+ a4-
This is closer to the actual order of scrambling. upper-case: pins up, lower-case: pins dows.
Another way to do the cube-in-cube : (R F2 L R F2 L' R2 [u'] [r'])4 (found by Per Kristen Fredlund). [u'] [r'] is turn around URF corner.
Also : (R U' R' U [r] [u])3 flips 3 corners and 2 edges, so (R U' R' U [r] [u])6 flips 3 corners and (R U' R' U [r] [u])9 flips 2 edges.