## solving the last sets of edges

here are the cases for the last two sets of tredges, split into cases with/without the parity

no parity

 simple match/flip this is the same case, just mirrored. it is probably the best and easiest case to end up with, and the easiest to understand. the idea is join the matching wing and edge (with the first d/d' turn) then take the edge out, and reinsert it upside down, then the unfold (last d/d') brings the final piece back into position and restores centers.

 double wing swaps this first case will swap two wings on one side, for the ones directly across while preserving orientation, the second alg swaps the same pieces, but flips orientation. The first alg is easier done for me with edges on FL and FR, while the second is easier with them on UF and UB, be sure to experiment with algs to see what works best for you.

 double edge flip This will flip two middle edges, same idea as the simple match/flip, except the centers are moved over instead of a wing. take it out, flip it upside down, put it back and restore. This is a good final case to get, also, using E/E' on the first turn is possible instead of slicing.

with parity

 single edge flip this is the single parity. it is similar to the revenge parity and the same alg can be used. There are a couple of algs for this case, but this one seems to be the most popular. you can usually avoid this case by itself with a good look ahead and instead get one of the easier parity situations.

 double parity this is a just like the double parity alg on revenge, it swaps the two groups of wings like the double wing swap, but it also flips one edge.

 edge flip/swap this parity is similar looking to the last two edges on revenge, just one side is a double. this will swap and flip the two remaining wings.

 checkerboard these patterns are easy to recognize since nothing is matched up, and the algs for them are also easy, usually faster than the single parity execution for me.

these cases are all the final edge configurations for the last two tredges, you don't need them all to be able to solve the 5x5 everytime, but its good to eventually learn them all. if you're looking at a minimum to learn, the recommended repotoire is single match/swap (and learn the double center flip at the same time, since its the same alg, just with a different starting and finishing move), regular double wing swap, single edge parity. after that the double parity, edge flip/swap and checkboards. finally the double wing swap/flip since it is the rarest case. these cases can sometimes be applied to individual groups in the last four to fix a tredge, however, regular pairing up as shown on the edges page requires many less moves than these cases. with some experimentation and practice the last four tredges can be pretty quick, and a great time to look ahead for the start of the 3x3 phase.

other useful algs and ideas

these next algs are useful for advanced last four edges strategies, one flips three centers (the ones at FU, FD, and BD). this alg can also fix the parity since it flips an odd number of centers.

the other is a simple M' U M idea, but when nothing good is visible to start with on the last four tredges, often that sequence will make an easy start somewhere. note that it create an edge three-cycle, and swaps the BU and BD wings. at first it will be hard to see where to apply it for best results, it will usually do something good if you just randomly apply it, after time the best cycle will become more apparent.

 flip 3 edges cycle edges and swap wings

 master final edges <15 there is no transitional delay between the first eight and last four edges, multiple pieces are placed at once intermediate final edges <30 sluggish finding the best way to finish, usually the technique is ok, but the look ahead is what needs the work beginner final edges 30+ its difficult to see what to pair up, and sometimes you undo previous matches accidently while pairing something up. practice is the key

on to the final solve

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copyright 2005 frank morris & clancy cochran