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Melbourne Cube Day 2010

I'm quite surprised you actually asked this. Surely you realise that more often than not, 8movers are more efficient than 9 or 10 movers, doesn't mean they always are.

What's so surprising? I simply want to see a concrete example rather than a baseless assumption. Also note that Chris' "!" insertion is just a silly way to do "."
 
Could you give an example of a 9-move insertion that would result in a shorter solution than if you inserted a 8-mover instead?

This does bring up a good point. No, I don't have a proof of this, but because it has not been disproven to my satisfaction, then I always check all insertions for a cancelation - even cases greater than 8 moves. I know what you mean that the "!" insertion is actually the same thing pretty much as "."

I have also found cases where an 8 move insertion (that does not cancel a turn) is the same as a 9 move insertion after the next turn that does cancel a turn (same net effect).

To answer your question I don't have a proof that any particular 9 mover cancels more moves than all 8 movers in a certain scramble. But, and to be fair, you also haven't provided a proof that all I need is 8 movers when checking for an insertion. Until I see such a proof, I will always check all length insertions to be safe.

Chris
 
This does bring up a good point. No, I don't have a proof of this, but because it has not been disproven to my satisfaction, then I always check all insertions for a cancelation - even cases greater than 8 moves. I know what you mean that the "!" insertion is actually the same thing pretty much as "."

I have also found cases where an 8 move insertion (that does not cancel a turn) is the same as a 9 move insertion after the next turn that does cancel a turn (same net effect).

To answer your question I don't have a proof that any particular 9 mover cancels more moves than all 8 movers in a certain scramble. But, and to be fair, you also haven't provided a proof that all I need is 8 movers when checking for an insertion. Until I see such a proof, I will always check all length insertions to be safe.

Chris

I have wondered about this and came to the exact same "conclusion" about CORNERS. Because I suck at corner insertions I have used Cube Explorer to find the best insertions for several FMC solutions that I couldn't find good insertions for myself (takes hours). Everytime I found a 9 move insertion that cancelled very well, it would turn into an 8 move insertion that cancelled 1 move less the next move. It isn't proof, but I suspect that you really only have to try 8 move insertions. I have also found that for a case that has an 8 mover there is about 2/3 chance that there is another 8 mover, but there are never more than 2 for any case.

For edges I have found that this is not true. I have found 10 movers (RURURU2R'U'R'U'R'U2 based) that cancel 4 moves that couldn't be reduced to 9 mover that cancelled 3 moves the next or previous move. And for many cases there are LOTS more than 2 cases to choose from, giving more chances of cancellations.

So far, I have only been able to use a GOOD corner insertion in competitions once. I suck at them. I can find them with infinite time, but for a 25 move skeleton it takes me 45 minutes. Edge-insertions I have used about 10 times and I can find them in about 20 minutes for a 25 move skeleton.

And I am now going to Tasmania for a short week and then "rectangularing" clockwise around the eastern half of Australia, starting in Melbourne as the Right-Down Corner.
 
Arnaud, how in the world did you get so much money that you can just travel the world and go wherever you please?? Whatever your job was, do you know if they are hiring?
 
So far, I have only been able to use a GOOD corner insertion in competitions once. I suck at them. I can find them with infinite time, but for a 25 move skeleton it takes me 45 minutes. Edge-insertions I have used about 10 times and I can find them in about 20 minutes for a 25 move skeleton.

What takes you so long? Do you use stickers? Recoging if a case is an 8-mover should be fast.
 
He borrowed some of my tape at MCD, which I read to do through his thread :P so I'd assume he does.
I just put the tape on, then do the solution slowly move by move, and wait for a situation where two stickers are interchangeable with 1 move, and so I can insert the non-interchangeable sticker, into one of the inter-changeable ones, do the swap with the interchangeable stickers, then undo inserting the sticker, then undoing the interchanging move.
The basic (x y x') z (x y' x') z'
Sorry if I didn't explain too well, but when I originally asked Zane_C about centre comms on a 4x4, this is what he showed me (several months ago). I understood instantly, and then understood on a 3x3 too. I'm actually the opposite of Arnaud, I suck at edge insertions, as I only know 1 sub 9 mover, and that's the 4 move STM/6 move HTM M' U2 M U2. I know a few different ways of doing this too. I also know Uperms, but I haven't found them to be too much use. And insertions to solve 4 edges, eg: M2 U2 M2 U2 or R2 U2 R2 U2 seem to hard to pull off, as there's more pieces. I can usually find a cancelling corner insertion in about 2 minutes, I find it very easy. AvG: any tips on edge insertions? :P
Edit: Don't get me wrong, I think that you'd know corner comms, I was just saying how I find them. I guess I kinda explained them too :P
 
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If you know optimal U, then you know a 7-mover: U M U2 M' U. It's the only one I've ever used for an edge insertion (I rarely do that and the 6-mover is rarer).
That's just the 6 mover with a setup. (or you could say Uperm missing the setup). When I said I only know M U2 M' U2, ofcourse I know the basic variants, that is pretty much exactly the same as M U2 M' U2, and anyone who knows M U2 M' U2 and not U M U2 M' U should really take a look in the mirror, and question thereselves on whether or not they should really be trying FMC when they don't see this. That 7 mover = the 6 mover. I wouldn't consider it a different case. This is one of the reasons I don't look for edge insertions, most use slice moves, so any "8-movers" (R U R' E R U' R' E') are no use while STM is not used in official competition. There are variants of M U2 M' U2, Uperm, and one 8mover, which I have temporarily forgotten (blah posted it in the FMC thread awhile ago), compared to many very different variations of corner comms.
But thanks for trying to help anyway :)
 
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