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I haven't seen any threads for critiquing 5x5x5 solves, nor is there apparently the popular Example Solve Game for the 5x5x5 where you solve the most-recent scramble, and post a subsequent scramble for someone else to solve.

B L2 2F' R 2R' U' 2L U' 3U' 2R'
L2 2L2 3R' D 2U' R' B 3U2 2D' R'
2R2 2D2 D 2F 3R' 3F R 3U R2 3U2
3F B 2B' 3R' 2L2 R 2U2 U' D 2R2
2F2 2L2 R' U2 3U' U' 2D 2L' 2D' 2U
U' 2U' 3U' 3R 2B R 2D' 3R 2F' B2
F2 L 2U R' 2R' 2F2 D B2 R' 2L
D2 L' 3U B' 2R' 3F' B F 2F' 2D
F2 L 2R2 3R' L' 3F' B' 3F 2F' F
3F' F' 2L' 2D' F 2R' 2F 2D' 3F' 2B2
3F2 2F' D' R2 U 2U' 2L 2U' L2 2F2
B2 F' 3F2 U2 3U L' B R2 2D' 2U'
U' 3U2 2B2 2F B2 D' 2F 2U' 3U2 F2
3F2 F2 3U B 3F' 2R2 2F2 U' 3U R'
2L2 F' 2U' B' 2D2 2L2 2B' 3F' F2 3R'
R D 3R2 2F 2D D2 2D B R' 3U2
2U2 R' B 2F2 L' 3F' F 2U' 2R' 2B
2D' R' U' 2F2 3R' 2F' 2R B' 2L2 2B2
2L2 R' B' 3R' D 2R' R' 2R2 F2 B
2L' L 2L' D' 3F2 R 2R 2D' R' 2B2

I think the reason there are no (or extremely few) critiques or reconstructions of 5x5 solves is because they involve so many moves that writing them up is laborious and error prone.

You might have more success with substeps. A few months ago I requested some edge-reduction only examples and several people contributed.

I haven't gone through it, but assuming what you posted above is a computer solution, that would hold little interest anyway for someone else to work through as an example because they would not learn anything useful to human solving.

I haven't gone through it, but assuming what you posted above is a computer solution, that would hold little interest anyway for someone else to work through as an example because they would not learn anything useful to human solving.

The first stage is probably of little interest because the program always finds the shortest corners solution and I don't think any human can make use of this. But people might still find that part interesting, since all 88 million+ corners are mapped to their most expedient solution.

The second stage is where I thought the most commentary would come in. The program has pre-solved 114,494,730 algorithms for cycling edges, midges, and tredges. This is, quite literally, every alg 12 moves (or fewer) deep. The program also has some 4-cycle, 3-cycle + 2-cycle, and 3-cycle + 3-cycle algs in its cluster. I am pretty sure most of these haven't been seen before. When they show up, maybe one or two of them could be of use to speedsolvers.

The third stage will be practically impossible for a human to make sense of. Some of the algs solve 27 centers at once, for example:

There's over 8 billion algs to solve every center configuration that is 11 moves from the solved state from the unsolved cage in the program's largest database.

L2 3U2 3F' 2L2 R 3F 2R' 2D B' 2U'
2L D 2U 3F' U' L2 3R2 3F2 L2 2D'
R 2D2 U2 3U' L D' 2U 3F L2 U
2F 3R' R F 2B' 2D D 2L2 B' L
2B2 2L 3R B2 3U D' 2U' 2F' 2B2 3F
2L' F' 2R' 3R' 3F' R L 3R' 2D' U'

The first stage is probably of little interest because the program always finds the shortest corners solution and I don't think any human can make use of this. But people might still find that part interesting, since all 88 million+ corners are mapped to their most expedient solution.

The second stage is where I thought the most commentary would come in. The program has pre-solved 114,494,730 algorithms for cycling edges, midges, and tredges. This is, quite literally, every alg 12 moves (or fewer) deep. The program also has some 4-cycle, 3-cycle + 2-cycle, and 3-cycle + 3-cycle algs in its cluster. I am pretty sure most of these haven't been seen before. When they show up, maybe one or two of them could be of use to speedsolvers.

The third stage will be practically impossible for a human to make sense of. Some of the algs solve 27 centers at once, for example:

There's over 8 billion algs to solve every center configuration that is 11 moves from the solved state from the unsolved cage in the program's largest database.

It's a little more complicated than connecting to an ODBC compliant database.

The database is presently about 92 GB and I load it into a RAM buffer when the centers-solving stage begins. As you can see, there are 8,247,064,891 algorithms (8.2 billion) that are pre-calculated. Most of them for centers-solving are of little use to humans, such as this one which solves 27 centers simultaneously:

I also added a "cascade solving mode." A picture can explain this better.

Each edge algorithm (in this phase) is accessible by an index, basically a number from 0 to 114,494,729 since there are 114,494,730 algorithms. I decided to write a recursive search routine where the index to the algorithm is passed in, rather than moves spawned by a move generator. The program "expands" the moves to the algorithm by simply going to the RAM location assigned to the index, and generating the moves found there.

There would be no way to examine all algs pairs up against all algs, but the program could pair every 4-move, 5-move, and 6-move alg against every one of the 114 million algs within a few hours. The 7-move alg list pairing would take a few days. You can see on the right of the screen is a number that shows 2.8 million algorithms are being processed per second. Since each algorithm is 18 moves long in this part of the solve, it's really equivalent to over 50 million moves/second being generated.

When you consider that depth 18 of the 5x5x5 has 370,667,354,480,380,735,149,206,536,695 positions total, and the program will finish its "depth 18" alg list in about 20 hours, the functional solving speed is 5,148,157,701,116,399,099,294,535 positions/second (5.1 septillion).

The result of a 6-move alg (shown in yellow) with a 12-move alg (shown in blue) that nets 16 edges being solved from a 300-move scramble is shown above. The numbers shown in parenthesis, {000000463} x {021970504}, are the indices of the current algs being tested to see if more edges are correctly solved. The moves associated with those algs appear to the right of them.

I was curious to see if the program could ever find a combination of two algs that would outperform finding the alg that nets the most edges solved twice in a row. In this case, it did, but the search took hours (and 6 fewer moves, which is pretty good).

This 300-move scramble, 8-move corner solve, and 16-move edge alg will recreate the position shown above:

L2 3U2 3F' 2L2 R 3F 2R' 2D B' 2U'
2L D 2U 3F' U' L2 3R2 3F2 L2 2D'
R 2D2 U2 3U' L D' 2U 3F L2 U
2F 3R' R F 2B' 2D D 2L2 B' L
2B2 2L 3R B2 3U D' 2U' 2F' 2B2 3F
2L' F' 2R' 3R' 3F' R L 3R' 2D' U'

using yau5 method. i don't know how well my efficiency stacks up, this solve seemed pretty average for the most part.

scramble: D' B2 D d U2 R' b L' d R' L u' r R' L b2 f B l L u r' f d r2 l' D' l' r' R F' U' b' R' b2 L' b B2 D' F2 U l2 u2 l2 D R2 r L B' U2 D b R2 L2 d2 b' U2 d' L u2

A 60-move scramble, by request:
L2 3U2 3F' 2L2 R 3F 2R' 2D B' 2U'
2L D 2U 3F' U' L2 3R2 3F2 L2 2D'
R 2D2 U2 3U' L D' 2U 3F L2 U
2F 3R' R F 2B' 2D D 2L2 B' L
2B2 2L 3R B2 3U D' 2U' 2F' 2B2 3F
2L' F' 2R' 3R'3F' R L 3R' 2D' U'

5x5 scramblers don't use triple wide turns. The centers need to remain stationary so that we can verify orientation mid-scramble, if need be. Also, it's just sorta awkward to do turns past half-way on a cube when you're reading a scramble.

Thanks for adding all of your notes. I am not familiar with yau5, but I'm interested in seeing as many different types of solves as possible. It is amazing to see completely different ways of looking at the puzzle in order to solve it.

I'll take a look at your scramble later this evening.