# 4x4 Linear Fewest Moves Challenge

#### StachuK1992

##### statue
I'm not actually interested in FMC for big cubes; I am making this thread with the hope that it will encourage users to create new, good big cube methods.

I simply don't think we have near-perfect big cube methods.

Rules:
-Don't take more than 20 minutes. There's no need for this to take longer, because it should be done linearly.
-I don't care what (Sign/WCA) notation you use; they're both fairly universal as far as I'm concerned.
If you don't specify, I'm assuming that r=slice, R=outer, Rw=fat/wide turn.
-200 moves max. Slice+wide turn metric.
(r2 = 1 move, as does R and Rw)

Have fun. Be creative ;D

statue

(Yes, I know that FMC tactics might not be the best for speedsolving methods. That's why I'm making you do it linear. Hehe)

#### theZcuber

I was actually just thinking about big cubes FM yesterday, but not linear!

#### StachuK1992

##### statue
It means you can't rescramble, and if you 'undo' a move, both the moves you did and the moves you did to undo those moves count against you.

#### Mike Hughey

##### Super Moderator
Staff member
Restricting to under 20 minutes might affect how practical it is to figure out a parity skip. (I know Chris Hardwick had some good ideas of how this might be achieved with a linear solve.) Give us an hour instead of 20 minutes, and I suspect it's very likely someone can come up with a consistent method for parity skip, but at 20 minutes, the time might be too tight to do all the counting that might be necessary.

#### StachuK1992

##### statue
Good! I don't want you to develop a way to detect parity skip!
I want the methods to be able to eventually used for regular solving. Too much time gives you too many impossible options that you couldn't take in a real solve.

#### Kirjava

##### Colourful
Give us an hour instead of 20 minutes, and I suspect it's very likely someone can come up with a consistent method for parity skip, but at 20 minutes, the time might be too tight to do all the counting that might be necessary.
Are you kidding? It's possible to completely avoid parity in normal speedsolves.

#### Lucas Garron

##### Super-Duper Moderator
Staff member
Are you kidding? It's possible to completely avoid parity in normal speedsolves.
Hmm. Do you get to see the scramble, Stachu?

Also, there was a while when we did this for the weekly competition (I think), but I'm not sure where that went.

#### StachuK1992

##### statue
Why would you need to see it? Sure, you can see it; just don't inverse it or do something similar.

One scramble, one solve.

#### Julian

##### Member
Why would you need to see it?
Because, I assume, they can count quarter turns (or something similar) in the scramble to figure out whether or not there will be parity. (Similar to counting quarter turns in a BLD scramble to determine if there will be parity.)

#### Kirjava

##### Colourful
No need to look at the scramble - edge cycles can be traced in ~10 seconds.

#### cmhardw

No need to look at the scramble - edge cycles can be traced in ~10 seconds.
I tried very hard to do this a few years back and could occasionally detect parity in under 15 seconds, but I usually averaged near 25-30 seconds. I did not trace the cycles of all 24 wings. I traced out the arrangement of always 12 cycles (with or without parity basically) it would take to reduce to a scrambled 3x3x3 with oriented edges.

If you have ideas on how to do the tracing in ~10 seconds I would be extremely interested in talking more with you! I've only managed to do this in under 15 seconds less than 10 times.

One anticipatory comment, if you do trace all 24 wings, then how do you handle cases such as where you have accounted for 20 pieces and are left with 4 remaining pieces (you know that none are solved)? It can sometimes take approximately 4-5 seconds just to locate one of those 4 pieces, let alone the cyclic structure of all 4.

It's not that I don't believe you, it's more that I'm completely at a loss for what your method would be! I would be very interested in taking this conversation to PM as well, since it is completely irrelevant to this thread (according to Statue's request).

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#### riffz

##### Member
I think he underestimated how long it takes to trace them, but his point was that given 20 minutes you can determine parity from the start relatively quickly without looking at the scramble.

Amiright?

#### Kirjava

##### Colourful
Not at all. I know of at least one person who can do it in under 15 seconds on average.

I'll PM you my ideas when I get home. I'll also do an FMC solve - I have some ideas for lowering movecounts.

#### Meep

##### Member
I might try this when I get home. Though I feel you should lower the max move count; I just counted the moves in a regular 5x5 speedsolve (with redux) and got 190.

#### RNewms27

##### Member
I might try this when I get home. Though I feel you should lower the max move count; I just counted the moves in a regular 5x5 speedsolve (with redux) and got 190.
This is 4x4.

Ah I see it now. Yeah limit should be ~150.

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