After the 4x4, solving "big" cubes is a little but simpler. The method remains very closely related to the 4x4 method: Solve the centers, then the edges, then the cube as a 3x3. On cubes that have an even cubie length (4x4, 6x6) you will ned to solve one center, then the related corners, then use the corners for reference to solve the other centers. This is beacuse there is no fixed center piece. On cubes with an odd cubie length, there is a fixed center for reference so you can solve the centers directly. You should not find it hard to adapt your edge piece mover formula for larger cubes. In the 6x6 and 7x7, you'll want to solve groups of edge pieces, then solve them as larger piece groups. You will want to experiment with it but it shouldn't be that hard to figure out what to do. One thing that might be a little bit tricky is the solving of the center piece. I will give you the example of a 5x5You will want to arrange it so that you have the pieces on the leading edge (the edge closest to you) as follows (LB is the edge that you are solving for, L represents the top color of the pieces that you are solving, X is a random piece). LXL You have a 2-and-2 sort of arrangement. Then bring the center piece L to the opposite side, but so that color B is on top. Now the situation is as follows: Leading edge: LLXLL, opposite edge: XBX. You should then apply the edge mover formula with the lefternmost 2 layers as one. Rotate the top layer twice and repeat. If you find yourself in a situation where there are 2 centers that are flipped, simply place them so that they are opposite of each other and apply the edge mover formula just using the 2 centers. This will not move them but just flip them in place.
Another tricky bit is parities. You will not encounter any "2 edge swap" parities on cubes with even cubie lengths, but you might encounter the dreaded edge-flip parity. If you examine the formula, you will see that it switches and flips the 2 edges in question. When the parity pops up on a 5x5, apply the formula but ignore the center. If you are trying to solve a 7x7 and the parity shows itself, the same idea can be applied. Say you have the parity on edge LB. Your situation is as follows: LBBBL. Use the formula ignoring the middle 3 layers. If it's a situation where everything is messed up (LBLBL) you will want to apply it twice: first, ignoring the middle layer and using the outer 2 layers as one, then secondly ignoring those middle 3 layers.
If you are having trouble solving the centers of a 7x7, here's a basic method: solve the 3x3 block, then the 4 triplets of center edges (the groups of three that suround the 3x3). Do this solving of the 4 center edge triplets on another face, then "store" them on a third until all 4 are solved. You can then insert them into their correct positions on the right face. The last 2 centers are tricky, but YouTube user Willdabeast6 has a great algorithm for placing those tricky pieces. It can be found at http://www.youtube.com/watch?v=X-Sc4pTPD0k . The formula is shown at around 8:30 but you'll want to watch from around 7:50 onwards to get the general ideas involved.
Another tricky bit is parities. You will not encounter any "2 edge swap" parities on cubes with even cubie lengths, but you might encounter the dreaded edge-flip parity. If you examine the formula, you will see that it switches and flips the 2 edges in question. When the parity pops up on a 5x5, apply the formula but ignore the center. If you are trying to solve a 7x7 and the parity shows itself, the same idea can be applied. Say you have the parity on edge LB. Your situation is as follows: LBBBL. Use the formula ignoring the middle 3 layers. If it's a situation where everything is messed up (LBLBL) you will want to apply it twice: first, ignoring the middle layer and using the outer 2 layers as one, then secondly ignoring those middle 3 layers.
If you are having trouble solving the centers of a 7x7, here's a basic method: solve the 3x3 block, then the 4 triplets of center edges (the groups of three that suround the 3x3). Do this solving of the 4 center edge triplets on another face, then "store" them on a third until all 4 are solved. You can then insert them into their correct positions on the right face. The last 2 centers are tricky, but YouTube user Willdabeast6 has a great algorithm for placing those tricky pieces. It can be found at http://www.youtube.com/watch?v=X-Sc4pTPD0k . The formula is shown at around 8:30 but you'll want to watch from around 7:50 onwards to get the general ideas involved.
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