Welcome to the Speedsolving.com, home of the web's largest puzzle community! You are currently viewing our forum as a guest which gives you limited access to join discussions and access our other features.

I know that these algs I gave were longer than what the optimal alg is, but, as I said, they are for a start. And, just because I have found the briefest pure edge flip in the world doesn't mean that I can find the briefest non-pure edge flip that meets your request.

By the way, I have a 21bqtm alg that takes a can take a 3x3x3 state "with a flipped edge" (that is, a reduced 3x3x3 on a 4x4x4 with odd edge parity) to solved.

By the way, I have a 21bqtm alg that takes a can take a 3x3x3 state "with a flipped edge" (that is, a reduced 3x3x3 on a 4x4x4 with odd edge parity) to solved.

The double parity that Jakub mentioned he uses to fix this dedge flip is actually a 4-cycle of 4x4x4 edges.

IMO - the main reason that the pure alg approach is running into trouble, is that it is forced to do a very specific 2-cycle that will also place the swapped edge pieces back into the original dedge. By not constraining this to just a 2-cycle (i.e. returning the edge pieces back to opposite sides of the same dedge location) should give an easier way.

In fact, any EVEN cycle (2,4,6,8,10) of the 4x4x4 edge pieces that make up the last 5 unsolved dedges will end up solving the flip parity, as long as the edge piece cycling ends up with paired dedges. This dedge pairing would normally be broken by these cycles, but here there is a solution because it is possible to target the piece cycles so that the dedges are reformed into their newly cycled locations.

The double parity is doing just that. By cycling 4 edge pieces (UFl-->UBl-->UFr-->UBr) the edge parity changes, and the dedge pieces also end up swapped as the natural consequence of this 4-cycle of edges. If the alg for this is nicer than the single parity one derived from 2-cycle edges, then the double parity alg should be the one used for fixing single parity as well.

This idea will work for other even cycles of 4x4x4 edges too. For example, the 6-cycle (UFl-->UBl-->URb-->UFr-->UBr-->URf) will fix edge parity, and at the same time move the dedges in a 3-cycle (UF-->UB-->UR). Note that the dedge parity in this case remains unchanged. It makes no difference though for this alg, since in practice, it takes too long to figure out if the dedge (PLL) parity is even or odd at this point in the solve. To just go ahead and change the dedge parity like the double parity does, or leave it the same like this 6-cycle, will end up being correct half of the time either way.

There are also 5 corners that can move, and do not have to be returned at the end of the alg. I don't even care what the corner parity is yet, since it will usually take longer to determine the corner parity here, than it will take to execute the alg that is used to fix it later on.

Should be no more excuses now. Somebody WILL get this.

UPDATE:
As a holiday special offer, I will now actually sell anyone the 19 outer block turn algorithm for the price of $1. That's right, for only $1 (and agreeing not to redistribute) you get to see the world's shortest known alg for OLL parity on 4x4x4. What a deal!

And of course, the 21q is still included! What are you waiting for?

Trade for any hand-found 23q pure OLL parity algorithms also accepted.