A135825 - OEIS

%I #9 Dec 11 2016 08:11:58

%S 121,184041,1521,53361,184041,1521,441

%N Moves to permute (ufl,ubr)(dfr,dbl) corners 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... The moves to permute (ufl,ubr)(dfr,dbl) corners are (D^2)*(R^2* D^2*F^2)*(R^2*F^2)*(R^2*U^2*D^2)*(R^2*D^2*F^2)*(R^2*F^2)*(R^2*U^2) = (11^2)*(3^2*11^2*13^2)*(3^2*13^2)*(3^2*7^2*11^2)*(3^2* 11^2*13^2)*(3^2*13^2)*(3^2*7^2) = 121*184041*1521*53361*184041*1521*441. 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. Joyner, J. Hopkins Press.

%e 441 = 3^2*7^2 codes R^2*U^2 moves.

%Y Cf. A135819, A135820, A135823, A135824, A135825, A135826, A135827.

%K fini,full,nonn

%O 0,1

%A _Giorgio Balzarotti_ & _Paolo P. Lava_, Nov 29 2007