Check out your spatial awareness. The puzzles below feature a 3 x 3 x 3 lattice of spheres. Each sphere bears one of seven letters (A-G). The letters represent the operations: Straight through (the null operation), Left, Right, Up, Down, Anti-clockwise roll and Clockwise roll. All you have to do is discover which operation is represented by which letter, such that a path starting at In 1 will end at Out 1 and so on. You can associate operations with letters by first clicking on a lettered button in the central column and then clicking on the button for the desired operation from right hand column. To display the effect of your choice, choose a particular input point using the Step button and then click Test. The red L-shaped markers represent heading (along a lattice line) and orientation. If you imagine that the L symbol represents a seat, then you sit astride the lattice line with the line perpendicular to it supporting your back. All entry points (In 1, etc.) start you off upright, that is to say with your head facing up. It doesn't matter which way up you are when you leave the lattice provided the co-ordinates and heading are correct. Remember, if you are flying horizontally but upside down, a Down operation will take you up. I find this hard, but the little L's help me a lot. Good luck.
Update:Pierre Baillargeon has supplied an enhancement which he finds helpful in keeping track of visited spheres. The left-hand column shows which spheres have been visited (when you press the test button) and the order of (first) visiting. His enhancement is the more remarkable as he produced it without the benefit of the original Java.
Credit. Andrea created a 4 x 4 puzzle with 4 operators. This is a simple (?) extension to that idea. I have abandoned her double-back operator as three dimensions mushroomed the two 90 degree turn actions into six and I felt that enough was enough. Graham.