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%I #16 Dec 11 2016 08:11:45
%S 14,14,98,56,56,392
%N Finite sequence of moves needed to flip the top uf, ub edges in a 3 X 3 X 3 Rubik's Cube.
%C r,l,u,d,f,b are respectively right, left, up, down, front, back faces of a 3 X 3 X 3 Rubik's Cube. Set M=2, R=3, L=5, U=7, D=11, F=13, B=17, where M is a 90-degree turn of the middle slice of Rubik's Cube; R is a 90-degree turn of the right face, L is a 90-degree turn of the left face...
%C The moves to flip the top uf, ub edges are (M*U)*(M*U)*(M*U)*U*(M^3*U)*(M^3*U)*(M^3*U)*U = (2*7)*(2*7)*(2*7^2)*(2^3*7)*(2^3*7)*(2^3*7^2) = 14*14*98*56*56*392; note that as the order of a 90-degree turn T is 4, then T^2 = T^-2 and T^3 = T^-1. Moves adapted from 'Adventures in group theory'.
%D D. Joyner, 'Adventures in Group Theory', John Hopkins Press.
%e For example, the number 14 = 2*7 encodes M*U moves.
%K fini,full,nonn
%O 1,1
%A _Giorgio Balzarotti_ & _Paolo P. Lava_, Nov 29 2007
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