A135824 - OEIS

%I #14 Dec 11 2016 08:11:54

%S 169,207025,4225,4225,1225,4225

%N Moves to permute (uf,ub)(ur,ul) 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... The moves to permute (uf,ub)(ur,ul) edges are (F^2)*(L^2*U^2*F^2)*(L^2*F^2)*(L^2*F^2)*(L^2*U^2)*(L^2*F^2) = (13^2)*(5^2*7^2*13^2)*(5^2*13^2)*(5^2*13^2)*(5^2*7^2)*(5^2*13^2) = 169*207025*4225*4225*1225*4225. 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 4225 = 5^2*13^2 codes L^2*F^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