cuBerBruce
Member
Technically, each of the sequences you found are two 3-cycles rather than two swaps, as is clear when I execute these sequence in GAP:
Code:
gap> U*F3*D2*B2*l3*B2*D2*F2*r3*F3*U3;
(6,38,11)(7,39,10)
gap> U*F3*l3*F2*D2*B2*r3*B2*D2*F3*U3;
(6,38,11)(7,39,10)I am not totally clear what you want. In terms of swapping all 4 center pieces on one face with those of another face, there is r2 f2 b2 r2 f2 b2. This swaps among opposite faces, and is actually 4 swaps as one might expect (with no hidden swaps or other hidden cycles). For 2 adjacent faces my solver gives:
Code:
Enter: 5uffuuff5u/8l8l/5f2u2f2u5f/8r8r/8b8b/8d8d
distance 1 node count 0 solved state checks 0
distance 2 node count 0 solved state checks 0
distance 3 node count 0 solved state checks 0
distance 4 node count 0 solved state checks 0
distance 5 node count 546 solved state checks 0
distance 6 node count 12792 solved state checks 240
distance 7 node count 220407 solved state checks 12336
distance 8 node count 5646369 solved state checks 1237992
distance 9 node count 57603123 solved state checks 7497474
Found solution: [10] l U2 B2 D2 l r D2 B2 U2 r
Found solution: [10] l D2 B2 U2 l r U2 B2 D2 r
Found solution: [10] l' F2 D2 B2 l' r' B2 D2 F2 r'
Found solution: [10] l' B2 D2 F2 l' r' F2 D2 B2 r'
Found solution: [10] r F2 D2 B2 l r B2 D2 F2 l
Found solution: [10] r B2 D2 F2 l r F2 D2 B2 l
Found solution: [10] r' U2 B2 D2 l' r' D2 B2 U2 l'
Found solution: [10] r' D2 B2 U2 l' r' U2 B2 D2 l'
distance 10 node count 881587164 solved state checks 138793824I also tried "swapping" individual center pieces among 4 faces, thinking I might get 2 swaps, but still ended up with double 3-cycles. (A couple solutions also changed the orientation of the cube.)
Code:
Enter: 5uf2u8u/8l2ld5l/5fu2f8f/8r8r/8b8b/8d2dl5d
distance 1 node count 0 solved state checks 0
distance 2 node count 0 solved state checks 0
distance 3 node count 0 solved state checks 0
distance 4 node count 0 solved state checks 0
distance 5 node count 177 solved state checks 0
distance 6 node count 8400 solved state checks 1782
distance 7 node count 62994 solved state checks 2403
distance 8 node count 2210466 solved state checks 493524
distance 9 node count 23569581 solved state checks 2312484
distance 10 node count 500716785 solved state checks 72125880
Found solution: [11] U u' L' f r2 f r2 f2 L U' u
Found solution: [11] U d' F' l b2 l b2 l2 F U' d
Found solution: [11] U d' F' l b2 l b2 l2 F u D'
Found solution: [11] u' D R' f l2 f l2 f2 R U' d
Found solution: [11] u' D R' f l2 f l2 f2 R u D'
Found solution: [11] u' L' U f r2 f r2 f2 U' L u
Found solution: [11] u' R' D f l2 f l2 f2 D' R u
Found solution: [11] D d' B' l2 f2 l' f2 l' B D' d
Found solution: [11] d' l' D l' f2 l' f2 l2 D' l d
Found solution: [11] d' r' B l' d2 l' d2 l2 B' r d
Found solution: [11] d' F' U l b2 l b2 l2 U' F d
Found solution: [11] d' B' D l2 f2 l' f2 l' D' B d
distance 11 node count 3033266855 solved state checks 594172323
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Just making sure the TFS databases I am recoding as matrix-case statement-for loop implementations have no errors in them, nor are there any "missing entries," and so on. I am just creating every position/orientation where the U face needs 2 centers to be solved, ditto for the F face. 
