[Help Thread] FMC Discussion

[Hypocrism]

I did my first proper attempt today, and got a 29.

U D L F R' B2 D R2 B R2 B2 U' F2 B2 R2 B2 R2 D' R2 F2

Solution:

R' (premove)
L2 F' L' D' (2x2x2)
U2 (premove)
R U R (block)
F2 R U' (block)
L' (premove)
R2 U R (block)
L D2 L' U2 L D2 L' U2 (insert)
U' L U' R2 F R'
(bold:cancellation)

Total: 29

It was actually quite exciting and novel!! I've read FMC stuff before but never tried to perfect a solve. Going to practise for Euros...

I've just come up with a way to systematically find a good (blockbuilding) start quickly (if there's any), that probably many good FMCers already use:

For each corner, find the 3 matching edges to see if there is a short way to make a square or a 2x2x2 block; if any, take note, but first look at all the other corners and do the same. After that, for each of the nice squares/2x2x2s you've found look if you can make other blocks while building them (this should be easier since you've already looked for possible good starts from other blocks).

Well, nothing revolutionary, but the key idea is that you can see all possible easy 2x2x2s very quickly.
What do you think? Do you already use this strategy?

I did this, and after choosing a good 2x2x2, I also tested out the possible premoves of the side that contained none of the initial 2x2x2's pieces. That got me a nice couple of blocks in few moves.

 

[ottozing]

I've just come up with a way to systematically find a good (blockbuilding) start quickly (if there's any), that probably many good FMCers already use:

For each corner, find the 3 matching edges to see if there is a short way to make a square or a 2x2x2 block; if any, take note, but first look at all the other corners and do the same. After that, for each of the nice squares/2x2x2s you've found look if you can make other blocks while building them (this should be easier since you've already looked for possible good starts from other blocks).

Well, nothing revolutionary, but the key idea is that you can see all possible easy 2x2x2s very quickly.
What do you think? Do you already use this strategy?

Very nice tip! I'll have to adapt something like this into my future fmc attempts.

What I've always done for fmc (or at least have done for a very long time) is check for every one move pair by doing every slice move once, checking for pairs, and repeating. Something I also like doing is finding all the one move pairs on inverse, and then using the inverse of that move as a premove for the normal scramble if I can't find anything good for it on inverse (and vise versa, if I can't find anything after any of my one move pairs).

 

[cmhardw]

I've just come up with a way to systematically find a good (blockbuilding) start quickly (if there's any), that probably many good FMCers already use:

... (tips and cool ideas)

That's a neat idea, I never thought to try that. I will certainly give that a shot on my next fewest moves attempt, seems like a great approach!

 

[TeddyKGB]

I did my first proper attempt today, and got a 29.

U D L F R' B2 D R2 B R2 B2 U' F2 B2 R2 B2 R2 D' R2 F2

I gave this same scramble a try and this is what happened:

On inverse

Pre move - B2

2x2x1: F D
2nd 2x2x1: R2 B' U
2x2x3: B' L' B
F2L -1: B R2 B' R'
2 Twisted corners: R' B R B' D' B' D' B D'

Skeleton on normal scramble: B2 D B' D B D * B R' B' R2 B @ R2 B2 L B U' B R2 D' F'

Insert at *: L B R' B' L' B R B' (6 moves cancel)
Insert at @: B' L B R2 B' L' B R2 (7 moves cancel)

Solution: B2 D B' D B D L B R' B' R2 B R2 B' L' B' L B U' B R2 D' F' - 23 moves

 

[Hypocrism]

I gave this same scramble a try and this is what happened:

On inverse

Pre move - B2

2x2x1: F D
2nd 2x2x1: R2 B' U
2x2x3: B' L' B
F2L -1: B R2 B' R'
2 Twisted corners: R' B R B' D' B' D' B D'

Skeleton on normal scramble: B2 D B' D B D * B R' B' R2 B @ R2 B2 L B U' B R2 D' F'

Insert at *: L B R' B' L' B R B' (6 moves cancel)
Insert at @: B' L B R2 B' L' B R2 (7 moves cancel)

Solution: B2 D B' D B D L B R' B' R2 B R2 B' L' B' L B U' B R2 D' F' - 23 moves

Nice one. I haven't looked closely at using inverse scrambles yet, although I understand the process, I've never quite worked out how it can find anything different to the regular scrambled state?

 

[Ranzha]

Nice one. I haven't looked closely at using inverse scrambles yet, although I understand the process, I've never quite worked out how it can find anything different to the regular scrambled state?

Watch.

Scramble: L' U' L F U' R U R' F'

You might realise that a solution to this scramble is the common OLL algorithm, F R U' R' U' R U R' F' with a U2 at the end.
Solution: F R U' R' U' R U R' F' U2

If you invert this solution and apply the result to a solved cube, you get the same scrambled state as you get with the original scramble sequence.
In the same way, if you invert the scramble sequence and then apply it to the state reached by first applying the inverted solution, you get a solved cube.

If your scramble is A and your solution is B, then (A B) is an identity (naturally), but so are (B A), (A' B'), and (B' A'). Also, (A A'), (B B'), (A' A), and (B' B) are identities.
A functions the same way as B'.
A' functions the same way as B.

But why would you ever invert?
Let's say you wanted to keep your original OLL-based solution as a back-up and wanted to explore the possibilities, so you use the inverse scramble (A') on a solved cube and reach a state.
If A = L' U' L F U' R U R' F',
then A' = F R U' R' U F' L' U L

You may recognise that a solution to this is a different OLL, L' U' L U L F' L' F, with a U at the end. Let's call this C.
Using the same principles as before:
If (A' A) is an identity, and (A' C) is an identity, then C functions the same way as A.
So, if we invert C and get C' = U' F' L F L' U' L' U L, then C' functions the same way as A', or a solution to A.

Thus our shorter solution of U' F' L F L' U' L' U L, which we didn't find when we only applied A, is the inverted solution of the state reached with the inverted scramble.

tl;dr You may solve the inverse scramble a different way than you would solve the scramble. The inverse of a solution to the inverted scramble is a solution to the original scramble.

 

[Hypocrism]

Watch.

Scramble: L' U' L F U' R U R' F'

You might realise that a solution to this scramble is the common OLL algorithm, F R U' R' U' R U R' F' with a U2 at the end.
Solution: F R U' R' U' R U R' F' U2

If you invert this solution and apply the result to a solved cube, you get the same scrambled state as you get with the original scramble sequence.
In the same way, if you invert the scramble sequence and then apply it to the state reached by first applying the inverted solution, you get a solved cube.

If your scramble is A and your solution is B, then (A B) is an identity (naturally), but so are (B A), (A' B'), and (B' A'). Also, (A A'), (B B'), (A' A), and (B' B) are identities.
A functions the same way as B'.
A' functions the same way as B.

But why would you ever invert?
Let's say you wanted to keep your original OLL-based solution as a back-up and wanted to explore the possibilities, so you use the inverse scramble (A') on a solved cube and reach a state.
If A = L' U' L F U' R U R' F',
then A' = F R U' R' U F' L' U L

You may recognise that a solution to this is a different OLL, L' U' L U L F' L' F, with a U at the end. Let's call this C.
Using the same principles as before:
If (A' A) is an identity, and (A' C) is an identity, then C functions the same way as A.
So, if we invert C and get C' = U' F' L F L' U' L' U L, then C' functions the same way as A', or a solution to A.

Thus our shorter solution of U' F' L F L' U' L' U L, which we didn't find when we only applied A, is the inverted solution of the state reached with the inverted scramble.

tl;dr You may solve the inverse scramble a different way than you would solve the scramble. The inverse of a solution to the inverted scramble is a solution to the original scramble.

This I get, but what I don't see is how it helps you to find anything different. Is the point really just to provide a different starting point to find ideas? Because if it is I certainly won't use it-within an hour I don't have near to enough time to explore all the possible blockbuilding starts from just the plain scramble. I don't need any more ideas, I need less!!!

Then again I might be missing something, and I think I need to try it out to see why it's so useful.

 

[dbax0999]

Thanks to Lars' Roofpig, I was able to easily embed cube animations showing user's solutions for the weekly FMC.

At this time it only support algorithms that produce solved cubes so I can't visualize the scrambles.

There's also an issue with the color scheme being messed up for solutions with rotations, I have a hack that can fix this but I haven't had time to implement it.

 

[Jakube]

This I get, but what I don't see is how it helps you to find anything different. Is the point really just to provide a different starting point to find ideas? Because if it is I certainly won't use it-within an hour I don't have near to enough time to explore all the possible blockbuilding starts from just the plain scramble. I don't need any more ideas, I need less!!!

Then again I might be missing something, and I think I need to try it out to see why it's so useful.

Yes, it's just to give you more possibilities.

But I don't think, this is a problem. You don't need to explore all starts on one side. Only the promising ones. If the scramble is bad, just try the inverse after a minute. It may be better.

Notice: The inverse looks similar to the normal. So if there is any 2x2 block on the normal, there will be also a 2x2 block on the inverse, but it may be on a different place with different colors. A lot of people use the inverse scramble not just as a different starting point, but during the hole solve.
So they build a 2x2x2 with A on the scramble S, then because the continuation sucks, go to the inverse A' S', where they extend it to a 2x2x3 with B, then go back to the normal with the Scramble B' S A, ... This is called NISS.

 

[porkynator]

My hats off to you, Sébastien. I couldn't choose a proper face mark from the list. :confused: :tu :fp

Now I update the history for the hardest scramble (list those who wrote down a full solution in this thread).
Scramble: F U' F2 D' B U R' F' L D' R' U' L U B' D2 R' F U2 D2

1. 35 HTM by Conrad (maybe first try, within 1-hour?)
2. 34 HTM by Tomoaki (within 1-hour) and shorten Conrad's solution to 32 HTM (no time limit)
3. Another 32 HTM solution by Tomoaki (no time limit)
4. 31 HTM by Guus (within 1-hour)
5. 30 HTM by Tomoaki (no time limit)
6. 30 HTM by Attila (no time limit)
7. 32 HTM by David (no time limit)
8. 29 HTM by Sébastien (within 1-hour)

If there's any omissions/missings, please let me know the solution.

In addition to the hardest scramble, I would like to share some hard scrambles here (Sébastien said in his post).

• Dutch Open 2009: R2 D B2 U B2 D B' D' R' U' F' D2 B2 R D L' B' F*
• by Cielo: L' R2 B2 D2 B2 R' B L' D' U F' L' F2 D' R2 B' U2 R F2 U'*
• FMC336: F' R U D' L2 F' B' U' B2 F2 L R' U D B2 F L R' B R' B D F2 R' D2 F' B' D U2 R
• FMC310: U' D2 L R' F2 R B D' F' B2 U' D' F' R2 L2 F U B' D2 U' B' L F2 U R D' B F R' U'
• FMC307: L' D B' D2 F' B U D' R F' D F' L B' D R' L' D F2 L D B2 F' U' L' R2 B' F L2 R
• FMC283: U' D2 B U L' B' F2 D2 L R U2 F' R' L2 D U2 F2 B' D' L' B' F2 U R B' F' R' U' B2 F2*
• FMC280: U' F2 U' D2 B2 U' B' F U' B L' U2 D' L' F2 B D2 B' L' B F R D R2 U R' F' U2 D R2
• FMC279: U' F' U2 B' L D' U F2 L2 B' U2 F2 B2 R U' B L U F' B' D U B R' B2 F R2 D2 L R2*
• FMC272: D2 L D' L2 U R' L2 B L R2 F D2 L R B' R F' R B' U' D L2 B' R D' R2 L2 F2 U' B*

Taken from this post and this post. Cielo's scramble may be the hardest in this list.
The mark '*' at the end means that no one has achieved Sub 30 AFAIK. Be first!

I've tried the hardest scramble today; DNF'd in the first hour, later I've found a 33 HTM solution:

Spoiler

Scramble: F U' F2 D' B U R' F' L D' R' U' L U B' D2 R' F U2 D2

With my NISS notation (moves in brackets are done on inverse scramble)
L' B2 //2 ce pairs (2/2)
(L B R' L' F') //2 squares (5/7)
D U' R + U2 B //2x2x1 + other blocks (5/12)
(D' F' D' F) //Pseudo F2L-1 + pair ready (4/16)
D2 L' U' L U //All but 3 edges and 3 corners (5/21)

Final skeleton and insertions:
L' B2 D U' R + U2 B D2 L' U' L U F' D F D F * L R B' L'
+ = D2 F' D F U2 D2 B' D' B U2 //3e, 3 moves cancel
* = F2 L B L' F2 L B' L' //3c, 3 moves cancel out

Final solution: L' B2 D U' R D2 F' D F U2 D2 B' D' B2 D2 L' U' L U F' D F D F' L B L' F2 L B' R B' L' (33 HTM)

IF cancels one more move, but its first insertion cancels only one move and the second one is inserted inside the first (= I would have never looked for it):
L' B2 D U' R U2 B [@1] D2 L' U' L U F' D F D F L R B' L'
Insert at @1: F2 D B D' F2 D B' D'
After the 1st insertion: L' B2 D U' R U2 B F2 D B D' F2 D [@2] B' D L' U' L U F' D F D F L R B' L'
Insert at @2: D' B2 U' D L2 U
Fewest moves: 32. 3 moves cancelled
The final solution: L' B2 D U' R U2 B F2 D B D' F2 B2 U' D L2 U B' D L' U' L U F' D F D F L R B' L'

I've also looked at other solutions and I've managed to improve Conrad's one to 31 moves:

Spoiler

Scramble: F U' F2 D' B U R' F' L D' R' U' L U B' D2 R' F U2 D2
F R L * B' + U' D' F //Conrad's EO (7/7)
U' R' D2 U L' U2 R' //A more efficient 2x2x3 EO (7/14)
D' L D' L' D L' //All but 2 corners 3-cycles (6/20)
* = L' F L B' L' F' L B //3c (4/24)
+ = R' U L' U' R U L U' //3c (7/31)

Insertions are optimal according to IF

I'm happy that I've managed to get a decent result, but I kinda feel like I've wasted an afternoon looking for insertions.

EDIT: Today I've tried the Dutch Open 2009 scramble...

Hi

After all the easy scrambles, here is a really hard one!
It was the scramble of the Dutch Open 2009 FMC competition october 17 2009:

R2 D B2 U B2 D B' D' R' U' F' D2 B2 R D L' B' F (18)

Winning solution was 35 moves bij Erik and me
(posting solution on request)

Gus

... and I've got a 25 moves solution in ~35 minutes!

Spoiler

Scramble: R2 D B2 U B2 D B' D' R' U' F' D2 B2 R D L' B' F

Pseudo 2x2x2 + pair: F2 R2 F2 U (4)
On inverse with premoves U' F2 R2 F2, complete 2x2x3: R U' R' B2 R' (5)
I've found this start quite early (5 minutes maybe, but I have also explored a bit another start). Back to normal scramble with premoves R B2 R U R', I changed my first moves to:
F2 R2 U B U' F' L' F' U //F2L in 9+5=14 wow!
Here at first I went for CLL (9 moves) + inserted edges 3 cycle, which was actually just a regular ELL inserted right after the CLL. Then I've found this finish:
R' B' D' B D R
D2 R F D F' D' R' //2 look LL (13)
R B2 R U R' //Undo premoves, 2 moves cancel (3)

Final solution: F2 R2 U B U' F' L' F' U R' B' D' B D R D2 R F D F' D' B2 R U R' (25 HTM)

I think this is one of my best solves ever, I am really proud of it.

EDIT 2: Got sub-30 also on Cielo's Scramble! My 50 minutes solution:

Spoiler

Scramble: L' R2 B2 D2 B2 R' B L' D' U F' L' F2 D' R2 B' U2 R F2 U'

With my NISS notation (moves in brackets are done on inverse scramble):
R' F' D L B' //2x2x1 + pairs (5/5)
(U B2) //Blocks (2/7)
U' R2 //Blocks (2/9)
(F' U2 F) //Blocks (3/12)
(D' F' R' F2 R2 F2 R2 F2 R' D R D') //All but 3 corners (12/24)
The part in italic is actually a edge double 2-cycle, as I've realized later, but I couldn't find anywhere else to insert it.
Skeleton (on normal scramble) and L3C:
R' F' D L B' U' R2 D R' D' R F2 R2 F2 R2 F2 R F D F' U2 F B2 * U'
* = F D' F' U' F D F' U //3c, 3 moves cancel (5/29)

Final solution: R' F' D L B' U' R2 D R' D' R F2 R2 F2 R2 F2 R F D F' U2 F2 B2 D' F' U' F D F' (29 HTM)

Yay!

EDIT 2.5:

Spoiler

IF finishes in 28 moves using my skeleton with the double edges swap left to be inserted:

R' F' D L B' U' R2 D R' D' F [@1] D F' U2 F B2 U'
Insert at @1: B2 U2 D2 F2 U2 D2
After the 1st insertion: R' F' D L B' U' R2 D R' D' F B2 [@2] U2 D2 F2 U2 D' F' U2 F B2 U'
Insert at @2: F' D' B' D F D' B D
After the 2nd insertion: R' F' D L B' U' R2 D R' D' B2 D' [@3] B' D F D' B D' U2 F2 U2 D' F' U2 F B2 U'
Insert at @3: D B2 U D' R2 U'
Fewest moves: 28. 9 moves cancelled
The final solution: R' F' D L B' U' R2 D R' D2 U R2 U' B' D F D' B D' U2 F2 U2 D' F' U2 F B2 U'

EDIT 3: I have found a 30 moves solution for the hardest scramble!

Spoiler

Scramble: F U' F2 D' B U R' F' L D' R' U' L U B' D2 R' F U2 D2
Premoves B' D B, on inverse:
F' D' R L
F R2 D'
B R2 B' D' F R //Pseudo F2L-1 (13/13)
F' U L' U2 L F //Pseudo F2L (6/19)
B U L U' L' B' U F2 //LL + adjust (8/27)
B' D B //Undo premoves (3/30)

 

[okayama]

Really great results for hard scrambles!
Now your number may be 30 because you got 30 for the hardest scramble.

FYI: Sébastien's results are here:

• Cielo's scramble
• Dutch Open 2009's scramble

My 1-hour solution for the Dutch Open is here. You're the 1st place for the scramble currently.

 

[porkynator]

Thanks! Yes, my number is also 30, for now (maybe I'll try that scramble again).
Thanks also for linking those solutions, they are very interesting. Sébastien got a bit lucky with that insertion on Cielo's scramble, but is blockbuilding is awesome :O

 

[Attila]

My solution for Conrad's scramble ( no time limit):

Spoiler

F2 B U B2 L R' U2 F' U L2 D' F2 L' D2 U2 L B F' D' U' L2 D2 U2 B' L2 25 HTM.

on inverse:
L2 B orient corners,
U2 D2 L2 U2 more 4 edges,
L R' @ F' L2 R2 B D2 more 2 edges,
R B2 L' D L2 F B' U2 L' U' D2 all but 6 centres,
insert at @: M S M' S' 7 moves cancel.
final (inverse) solution:
L2 B U2 D2 L2 U D F B' L' U2 D2 L F2 D L2 U' F U2 R L' B2 U' B' F2

 

[Cubenovice]

Atilla, on Cielo's scramble you can solve the corners in 6 moves and if i remember correctly leave 8 edges in 13 moves.
Perhaps an interesting scramble for you?

 

[Renslay]

I just submitted a solution.

Hm, maybe I'm going into FMC in the future...

 

[Attila]

Atilla, on Cielo's scramble you can solve the corners in 6 moves and if i remember correctly leave 8 edges in 13 moves.
Perhaps an interesting scramble for you?

Yes, it's seems interesting, although not too easy.
I found this solution in 90 mins:

Spoiler

premoves: F2 R2 U'
F' B' D2 R' L' all corners and 2 edges( + 2 pseudo edges on UL UR places)
U2 B' U2 D2 F more 2 pseudo edges,
U' R2 D makes pseudoness,
F2 L' B2 D' U R2 B
L2 U' L2 D2 LSE.

 

[kinch2002]

Welcome to Cambridge: D2 L2 D L2 B2 U F' U' F' L F' R U2 R2 F2 L F2 B2 R2

26 moves: D2 F2 L F' D F' R F D F D2 L D' L' F' D2 B2 U B U2 B D2 B' U2 B D2

Square: D2 L
Add premoves to make that a 2x2x2 block
So, normal scramble with premoves B2 U B2
The luck starts here
2x2x3: D2 F2 L F' (7)
F2L-1: D F' R F (11)
F2L: D F D F' (15)
Leave 3 corners: F D L D' L' F' D2 (19)
Skeleton: D2 F2 L F' D F' R F D F D2 L D' L' F' D2 B2 U B2 (19)
The luck ran out. Insertion only cancelled one move in a few places

Lucky

 

[porkynator]

Hi fellow FMCers, I have started a website dedicated to FMC: http://fmcsolves.altervista.org/
Thread on his forum

 

[cuBerBruce]

Hi fellow FMCers, I have started a website dedicated to FMC: http://fmcsolves.altervista.org/
Thread on his forum

This reminds me of another FMC database issue. Per Fredlund was hosting a weekly FMC contest, and one could look at all the past solutions. But now that the contest is no longer running, there seems to be no way to view the database of past results. Does this database still exist? Is there any way to access it? Could it be made available as some sort of data file? I think there would be several solves from that database that would good to include on porkynator's site.

 

[TheDubDubJr]

So interesting situation that happened.

Jay McNeill, Ryan DeLine and I did a skype group FMC attempt (separate) with this scramble.

Scramble - B2 L2 B2 L' B2 L F2 D2 R2 D L2 D' B2 R2 B2 F' L2 R2

Jay and I ended up with 28s.

I did
n: R2 L F2 U2 B' U2 B2 R2 F U2
switch
i: F' R2 F' R' D R' D' R' D R D' R2

so my skeleton was
R2 L F2 U2 B' U2 B2 R2 F U2 R2 D R' D' R D R D' R F R2 F

After the hour was up we showed each other our attempts and Jay had an alternative skeleton like this.
R2 L B2 D2 B' D2 F2 R2 F U2 R2 D R' D' R D R D' R F R2 F

I quickly looked at both skeletons and thought they were exactly the same.
I looked at IF afterwards and saw my skeleton gave a 28 optimal (which is what I ended up with).
I remember Jay saying he found a 22 to 3corners that IF said 27 was optimal.

After figuring out that
R2 L F2 U2 B' U2 B2 R2 F U2 R2 D R' D' R D R D' R F R2 F
R2 L B2 D2 B' D2 F2 R2 F U2 R2 D R' D' R D R D' R F R2 F
are different, BUT do exactly the same thing.
But the second one yields better insertions.

I just thought this was a very interesting situation and could be used to find better insertions.

Spoiler: Anonymous Moose

Like at Michigan, got a DNF