my third php project is a recursion exercise which gives solutions to
the rubik's cube. the purpose is to deal with modeling and transformation in php.
presently, the cube is displayed as if unfolded. the
solution to the problem displayed appears directly below. eventually i will provide a form
where a problem can be entered and solved. for now the problem must be entered in the program.
Third PHP Project:
solution:   5. YC   4. RW   3. BW   2. WC   1. OC  
center squares rotate in place, and the sides are thus named Y=yellow, G=green, etc.
the direction of rotation is named: C=clockwise, and W=counterclockwise. when reading
the solution steps above, for example, GW means rotate the green face
counterclockwise.