unsolved
Member
I ran my brute force 4x4x4 solver on an entirely-finished cube except for a single center on the U and F faces (mostly for optimization and speed testing). Every center configuration can be solved in exactly 8 moves. Here is the data if anyone is interested.
Code:
Center scenario U1:F1 solved after 722,657,630,017 nodes by: u L' u' l u L u' l'
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|####|OOOO|####|####| |OOOO|####|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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Center scenario U1:F2 solved after 25,060,299,743 nodes by: U r U' l' U r' U' l
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|OOOO|####|####| |OOOO|OOOO|####|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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Center scenario U1:F3 solved after 34,111,149,775 nodes by: U b d' b' U' b d b'
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|OOOO|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|####|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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Center scenario U1:F4 solved after 36,601,594,190 nodes by: U l' d2 l U' l' d2 l
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|OOOO|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|####|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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Center scenario U2:F1 solved after 33,786,950,785 nodes by: U b u b' U' b u' b'
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|OOOO|####| |OOOO|####|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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Center scenario U2:F2 solved after 723,853,410,535 nodes by: u L u' r' u L' u' r
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|OOOO|####| |OOOO|OOOO|####|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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Center scenario U2:F3 solved after 25,973,341,490 nodes by: U r d2 r' U' r d2 r'
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|OOOO|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|####|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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Center scenario U2:F4 solved after 32,943,679,535 nodes by: U b' d b U' b' d' b
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|OOOO|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|####|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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Center scenario U3:F1 solved after 22,089,356,201 nodes by: U f u' f' U' f u f'
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|####|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|OOOO|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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Center scenario U3:F2 solved after 36,277,395,200 nodes by: U l' u2 l U' l' u2 l
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|####|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|OOOO|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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Center scenario U3:F3 solved after 765,444,600,500 nodes by: u' f u F u' f' u F'
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|OOOO|####|####| |OOOO|####|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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Center scenario U3:F4 solved after 23,482,897,075 nodes by: U f' d' f U' f' d f
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|OOOO|####|####| |OOOO|OOOO|####|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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Center scenario U4:F1 solved after 25,747,270,856 nodes by: U r u2 r' U' r u2 r'
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|####|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|OOOO|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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Center scenario U4:F2 solved after 23,256,826,441 nodes by: U f' u f U' f' u' f
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|####|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|OOOO|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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Center scenario U4:F3 solved after 22,315,426,835 nodes by: U f d f' U' f d' f'
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|OOOO|####| |OOOO|####|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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Center scenario U4:F4 solved after 727,561,803,916 nodes by: u f' u' F' u f u' F
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|OOOO|####| |OOOO|OOOO|####|OOOO| |XXXX|XXXX|XXXX|XXXX|
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|####|####|####|####| |OOOO|OOOO|OOOO|OOOO| |XXXX|XXXX|XXXX|XXXX|
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BOTTOM BACK LEFT
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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|~~~~|~~~~|~~~~|~~~~| |&&&&|&&&&|&&&&|&&&&| |^^^^|^^^^|^^^^|^^^^|
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