Orlow's 4x4 Solution

Solution

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Welcome to the Rubik's Revenge solution! 

There is a specific order to follow when solving the Revenge.  First solve the centers.  Then pair the edges.  After that, you can solve it like a 3x3 until (if, that is) a parity occurs.  This means in the end either one edge pair is flipped or two corners are swapped.  These are both impossible on a 3x3.

Solving the Centers:

It is pretty easy to solve one center without any algorithms.  But for the others, use this algorithm.

To switch these two centers:

centers.gif

Perform this algorithm:

centerswitch.jpg

Use this algorithm as necessary to swap the centers around.  Also, unlike the 3x3, the centers are not fixed, and they can be on any side.  So you have to use the corners to be able to tell which color to use.  For example:

corner.jpg

In this case, the top face would be blue, the right yellow, and the front red.  If you have three centers like this, then the others don't require a corner, because all you need to remember is which side is opposite what.  Bule and green and always opposite, so are yellow and white, and red and orange.

Once the centers are done:

Solving the Edges:

The edges don't necessarily need to be in the right place, they just need to be paired for now.  So there is an algorithm used to cycle three edges. 

To perform the 3-edge cycle:

edgecycle.jpg

edges.gif

In the above picture, the 3-edge cycle will cycle the 3 edges shown with arrows.  If the bottom edge is the other blue yellow edge, you would want to position it so the top blue yellow is on the left side of that top front edge, and the bottom one is on the right of the bottom front.  Do the edge cycle, and the edge on the bottom will move to the top, placing itself next to the one on top, pairing the edge.  Do this for all edges, and when pairing an edge, make sure there are NO ALREADY PAIRED EDGES ON THE RIGHT EDGE.

If you only have two scrambled edges left:

2edge.gif

Use the edge cycle to scramble the solved edge and keep the other two scrambled.  That way, you have three scrambled again, and you can turn the three edges so that you can do the edge cycle to solve all 3 at once.

Once you have all the edges paired, You can proceed to solve it like a 3x3 until (if) one of the two parities occur.  These are having one edge pair flipped, or having two corners that need to be swapped.  If they don't happen, then you're fine!  If they do, click the link below to be taken to the parity fix page.

Parity Fixes

How to solve the Rubik's Revenge-
Brian Orlow