# Message #3103

From: Melinda Green <melinda@superliminal.com>

Subject: Re: [MC4D] New 3^4 shortest solution! (227 twists)

Date: Sat, 04 Apr 2015 12:36:10 -0700

I was wondering if anyone would mind that I update the record. I suppose

it’s valid because we allow people to save solution states and revert to

them as needed. I guess I’ll plan to update the solution date as well

unless anyone objects. BTW, a solution time measured in years is

unlikely to get a speedsolving prize unless it’s for the *slowest* solution!

-Melinda

On 4/4/2015 5:59 AM, damienturtle@hotmail.co.uk [4D_Cubing] wrote:

>

>

> This was just for a random scramble generated by MC4D, I never tried

> to get an unusually good or bad scramble, I took the first one

> generated. 200 is just a nice milestone, in my own opinion, so there

> is no real significance to the 200 moves I mentioned as far as I know.

>

> I sent the solution to Melinda last weekend (it’s taken me this long

> to type up the post) but it doesn’t seem to have been updated in the

> HOF yet so I realise the log file isn’t available to look at.

>

> Matt

>

>

> —In 4D_Cubing@yahoogroups.com, <ed.baumann@…> wrote :

>

>

> This is not the shortest solution for a specific scrambling but for

> the worst case scrambling.

> If ‘gods number for 3^3 got under 20 you try ‘under 200’ for 3^4 now.

> Correct?

> Ed

>

> —– Original Message —–

> *From:* damienturtle@… [4D_Cubing]

> <mailto:damienturtle@…%20[4D_Cubing]>

> *To:* 4D_Cubing@yahoogroups.com <mailto:4D_Cubing@yahoogroups.com>

> *Sent:* Saturday, April 04, 2015 2:10 PM

> *Subject:* [MC4D] New 3^4 shortest solution! (227 twists)

>

> Hi everyone,

>

> For those newer members, I used to be fairly active here a few

> years back and set the 3^4 fewest moves record with 251

> twists, amongst other things. I’m not actually returning to

> being active (I probably won’t be taking part in the

> speedsolving contest being talked about, much as I would like

> to), I just felt like tidying up this solve since I hadn’t

> finished optimising the last step before, but when I became

> busy I just submitted what I had so far. Essentially, I had

> ended with a parity situation which cost moves to fix, and I

> wasn’t happy with that. After going to a speedsolving

> competition recently (I had a free weekend and had fun even

> though I was very out of practice) and having good luck in FMC

> with a 28 twist solution (which should have been 25 twists,

> maybe if I had practiced at all I would have spotted the

> really obvious insertion that I missed), I decided to correct

> the ending of my 3^4 solution with something much better,

> thoug h I’m still busy these days so I could probably have

> found something even better if I was willing to spend longer

> on it.

>

> I’ll try to explain roughly how my solution works, especially

> since the ending now isn’t very clear now that I’m better at

> fewest move solving. The first 182 twists of the solution are

> unchanged from before, since I didn’t really have the time to

> work through a full solve and because I always considered my

> previous submission as an unfinished solve which I wanted to

> finish eventually. It is simple blockbuilding mostly, followed

> by orienting the last layer. This means that what is left is

> essentially a 3^3 solve embedded into the 3^4 puzzle, and it

> is this which I revisited. As for the parity problem I had,

> try doing a U2 move on one 3^3 cell, leaving the rest of the

> puzzle solved, my best solution for this is 22 twists if I

> remember correctly.

>

> Optimising the last step is weird. It’s based on optimising a

> 3^3 solve, but it’s not quite as simple as that. Let’s look at

> that first though, and the metric used (as a simplification

> since the ‘correct’ metric is too complicated) is

> quarter-slice turn metric. A quarter turn of any layer is one

> move, a half turn of any layer counts as 2 moves. For some

> orientation I happened to choose, I looked at what the 3x3

> scramble was, and used CubeExplorer to find a short scramble

> to work with:

>

> D L2 F D2 U’ F U’ F D’ U’ R’ B2 L’ B F’ U’ B U’

>

> Now, due to the 3^4 context and my solution before this point,

> I needed to perform a net result of an L turn, which in

> practice means the net result of adding the twists of the

> solution (ignoring which faces are turned) must be a quarter

> turn clockwise (so L, R, U2 B’, L’ F’ D’, etc. would be valid

> solutions in this regard). Also, by being able to change the

> previous twist in the solution, I get a free turn of the front

> face in terms of movecount, which I tak e advantage of. My

> solution looks like this (knowledge of FMC techniques

> required, I can explain in more detail if anyone wants me to):

>

> (F) R’ (U’ D) L F’ //222 block 4/4

> U’ L2 U L D //223 block, 6/10

> (B’ L D L D’ L’ U’ L U L2) //Performed on inverse, solves all

> but 4 corners + 3 edges, 11/21

>

> Skeleton: (F) R’ (U’ D) L F’ U’ L2 * @ U L D ** L2 U’ L’ U L D

> L’ D’ L’ B //21 moves

> Insertions:

> * = (F B’) U’ L U L’ (B F’) //Solves 3 edges + 1 corner, no

> moves cancel, 6/27

> @ = L U R’ U’ L’ U R U’ //Solves 3 corners, 2 moves cancel, 6/33

>

> Solution: (F) R’ (U’ D) L F’ U’ L2 (FB’) U’ L U L’ (BF’) L U

> R’ U’ L’ U R L D L2 U’ L’ U L D L’ D’ L’ B //33 moves QSTM

>

> Bonus: insert ** = D’ (LR’) B L2 B’ (RL’) D L2, to solve 3

> edges, which cancels 7 moves. Never really checked the corner

> insertions on this, so it might have given a better result

> actually, but probably not.

>

> Now, I just try to adapt this to the 3^4 solve as efficiently

> as possible. My first serious attempt managed 230 twists, then

> 229. After a while I found a 228 twist solution which I nearly

> kept, but some instinct told me that I could save one more

> twist, which I managed to do.

>

> The idea is as follows. Say we need to do R U R’ U’ to solve

> the 3^3. The simple solution is to do R [F] R [F]’ R’ [F] R’

> [F]’ (8), where [F] means to rotate the whole cube as in an F

> turn, and notice that if we ignore the rotations all the moves

> cancel, which is necessary. I think Ray put some info on this

> on the wiki for how this works, if you aren’t familiar with

> it, try doing these moves on the ‘inside’ face in the most

> obvious way, with one twist in MC4D for each twist and for

> each rotation. Instead, we could do R U [UR] U’ R’ [UR] (6),

> where [UR] rotates the cub e around the axis though the UR

> edge and the opposite edge DL, and again all moves cancel once

> rotations are ignored. With this idea, two moves are saved

> here, and for full solutions the same idea applies but it

> becomes far more difficult to optimise. With this, my solution

> turned out to be:

>

> [F] F’ M’ [F]’ R B’ U’ R2 S R’ [UL] R D [DR] D’ S’ R U [DR] U’

> L’ D’ [F]’ D L R U R [F]’ U [UR] U’ R’ U R D [UFL] D’ [RB] R’

> U’ [DR] B

>

> where S is a slice turn which follows F, M is a slice turn

> which follows L, and [UFL] is a clockwise cube rotation about

> the UFL corner.

>

> I didn’t do this on paper, I worked in MC4D, then typed up

> what my final solution was. The strangest part for me was

> trying (R z’ U), which is essentially a double turn with a

> rotation in the middle, which actually saved a rotation overall.

>

> I think I’m unlikely to try beating this, so if anyone wants

> to take the record, they are welcome to it. I just hope I’ve

> made it very challenging to do so :), but it is certainly

> possible. I reckon sub-200 twists is very possible, so maybe

> if this isn’t achieved for many years, I might try to do it

> myself …

>

>

> These days, I’m doing a PhD is mathematics, working on network

> theory. I seen that someone new here recently is also in this

> area, so I might be able to have an interesting conversation

> with them :). I have one paper recently resubmitted to a

> journal which will hopefully be accepted soon, and another

> related paper nearly ready to be submitted. This is why I

> don’t have much time to spend on cubing, but that’s life.

>

> I hope as many people take part in the speedsolving contest as

> possible, it was very fun the first time so I recommend having

> a go. Even though I won’t have time to practice for it, I’ll

> be interesting in the results so please make them exciting!

> Good luck everyone!

>

> Happy hypercubing,

> Matt</ p>

>

>

>

>