Solving Rubik's Cube

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5x5x5 Solution

WARNING! My complete solution for the 5x5x5 (Professor's) Cube is on this page. If you haven't already solved it yourself then I recommend that you skip this page.

Step 1: Solve the centers.

This is the only part of solving the 5x5x5 cube that is potentially more complex than solving the 4x4x4 cube. And that's only because there are nine sub-cubes in a 5x5x5 center where on the 4x4x4 cube there are four. On the other hand, on the 5x5x5 cube you've always got a center sub-cube to use as a reference, and I find that most people can solve the centers without help if they just work at it long enough.

To solve the centers there are really only two variations of the one same move that you need to know.

3 face shuttle (a)	3 face shuttle (b)

l’ b’ l b U b’ l’ b l U’	l’ β ’ β U β’ l’ β l U’ *

*I'm using the Greek symbol β (beta) here to mean one row farther in from the b row (the center one). This is the only place that I'll be using this notation.

Notice that these are really both derivatives of the same sequence. The first four moves exchange six center pieces. (This same move is often used on 3x3x3 cubes to make a "circles" pattern on all the faces after the cube's been solved.) Then the up face is turned one quarter turn and the previous moves are reversed. The net result is shown in the diagram.

I typically solve one or more faces using simple, trivial moves that may also disturb the other faces, then I rotate the cube and use this move to solve all the squares in each of the other faces in turn.

Note that since you don't care about mixing corners and edge pieces, you can rotate all of the faces as much as you like between turns to properly set up the sub-cubes for the next move.

Step 2: Mate edges.

Once all the centers are solved, the next step is to put together all the edge pieces in groups of threes. The following move is useful for that purpose.

3 piece shuttle

Full: l’ U R U’ l U R’ U’
Simplified: L’l’ U R U’ Ll

The full move does exactly what's shown in the diagram. The simplified move does the same basic thing but it moves the edges and corners around a bit. Since at this stage of the game, we only care about mating the edges, go ahead and use the simplified move.

(Note that Ll is simpler than l by itself because it's easier to just turn the two rows together as a unit than it is to turn the l row by itself.)

You will almost certainly need to rotate some of the faces to line sub-cubes up so that you can mate all the edges but again, that's not a problem because we don't really care where the edges end up so long as they're all together.

I typically use this move by rotating the cube so that the the center FU sub-cube and the sub-cube to it's left don't match. Then I rotate the other faces until the FU center sub-cube's mate is in the upper FR position. Make sure that the colors of these two sub-cubes match on the F side. Also, at the very least, make sure that it's OK to disturb left BU sub-cube. Better still, try and find the center edge piece that will match the left FU edge after the move has been completed. That way you can put two pieces in place at once.

If you keep executing this move then eventually one of two things will happen: either you'll end up in a state where all the edges are mated or you'll end up in a state where all are mated but two and no amount of work with the 3 piece shuttle move will mate all the edges. If that happens, then orient the cube so that the two troublesome edges are in the UF(left) and UB(left) positions and execute this move:

4 piece shuttle

(r U2)x4 r

Now use the 3 piece shuttle to put the remaining 3 pieces into place and you're ready to move on.

Step 3: Solve as a 3x3x3 cube.

At this point, with the centers solved and all the edges mated, you've basically just got a fancy 3x3x3 cube. Solve it as you would a normal Rubik's Cube and you're done!