coolcomputery
Member
6x6 GN is at most 101.
I reduced the GN of 4x5->5x5 + 5x5->6x6 to 38, by applying at most 5 prefix moves to every scramble that would naively take >38 moves. There were 249347110 total scrambles, which took 4294.610 seconds to process (including making the two BFS trees). Referring to this earlier post, this means that the GN of 6x6 is at most 27 (0x0->2x2->3x3) + 21 (3x3->4x4) + 15 (4x4->4x5) + 38 (4x5->5x5->6x6)=101.
I've also rewritten my BFS tree and tree optimization programs and put them on https://github.com/coolcomputery/Loopover-Brute-Force-and-Improvement
UPDATE (2021-06-27): 6x6 GN is at most 100.
This time I reduced the GN of 4x4->4x5->5x5 to 28, by applying at most7 prefix moves 6 prefix moves. There were 709300008 total scrambles, which in total took 3167.242 seconds 42296.808 seconds. by applying at most 6 prefix moves. Thus, 6x6 GN is at most 27 (0x0->2x2->3x3) + 21 (3x3->4x4) + 28 (4x4->4x5->5x5) + 24 (5x5->6x6)=100.
Doing 4x4->5x5 brute-force requires tracking 20!/11!=~60 billion states, which is too big for Java arrays to be use to track whether a state has been visited before or not during the BFS. It might be possible to replace Java arrays with several thousand or so I/O files, but that will take a lot of work to program and will probably result in a very slow BFS.
UPDATE (2021-06-28): 6x6 GN is at most 99.
I further reduced the GN of 4x4->4x5->5x5 to 27, by applying at most 7 prefix moves. There were 2821027911 total scrambles, which took 16478.048 seconds to process. 27 (0x0->2x2->3x3) + 21 (3x3->4x4) + 27 (4x4->4x5->5x5) + 24 (5x5->6x6)=99.
UPDATE (2021-06-29): 6x6 GN is at most 98.
This time I reduced the GN of 0x0->2x2->3x3 to at most 26. 5629775526 total scrambles took 28655.157 seconds to process. 26 (0x0->2x2->3x3) + 21 (3x3->4x4) + 27 (4x4->4x5->5x5) + 24 (5x5->6x6)=98.
Currently, trying to reduce 4x4->4x5->5x5 to 26 moves results in java.lang.OutOfMemoryError because my program is forced to try generating all prefix move sequences consisting of 9 moves.
I reduced the GN of 4x5->5x5 + 5x5->6x6 to 38, by applying at most 5 prefix moves to every scramble that would naively take >38 moves. There were 249347110 total scrambles, which took 4294.610 seconds to process (including making the two BFS trees). Referring to this earlier post, this means that the GN of 6x6 is at most 27 (0x0->2x2->3x3) + 21 (3x3->4x4) + 15 (4x4->4x5) + 38 (4x5->5x5->6x6)=101.
I've also rewritten my BFS tree and tree optimization programs and put them on https://github.com/coolcomputery/Loopover-Brute-Force-and-Improvement
UPDATE (2021-06-27): 6x6 GN is at most 100.
This time I reduced the GN of 4x4->4x5->5x5 to 28, by applying at most
Doing 4x4->5x5 brute-force requires tracking 20!/11!=~60 billion states, which is too big for Java arrays to be use to track whether a state has been visited before or not during the BFS. It might be possible to replace Java arrays with several thousand or so I/O files, but that will take a lot of work to program and will probably result in a very slow BFS.
UPDATE (2021-06-28): 6x6 GN is at most 99.
I further reduced the GN of 4x4->4x5->5x5 to 27, by applying at most 7 prefix moves. There were 2821027911 total scrambles, which took 16478.048 seconds to process. 27 (0x0->2x2->3x3) + 21 (3x3->4x4) + 27 (4x4->4x5->5x5) + 24 (5x5->6x6)=99.
UPDATE (2021-06-29): 6x6 GN is at most 98.
This time I reduced the GN of 0x0->2x2->3x3 to at most 26. 5629775526 total scrambles took 28655.157 seconds to process. 26 (0x0->2x2->3x3) + 21 (3x3->4x4) + 27 (4x4->4x5->5x5) + 24 (5x5->6x6)=98.
Currently, trying to reduce 4x4->4x5->5x5 to 26 moves results in java.lang.OutOfMemoryError because my program is forced to try generating all prefix move sequences consisting of 9 moves.
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