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[Help Thread] FMC Discussion

Here's another one: what are the odds to run into a situation where you require three cycles to solve the last 5 corners?

On this weeks FMC I found two completely different starts to leave 5 corners and both of them required three cycles to solve:
Both solves had one twisted corner and two pairs of corners that required swapping.

FMCFMCL...
 
Cubenovice said:
Here's another one: what are the odds to run into a situation where you require three cycles to solve the last 5 corners?

On this weeks FMC I found two completely different starts to leave 5 corners and both of them required three cycles to solve:
Both solves had one twisted corner and two pairs of corners that required swapping.
Click to expand...

I'll assume you're solving F2L minus one slot, then solving the remaining edges completely ignoring the remaining corners. This would give (5!/2)*(3^4) = 4860 possibilities for the last 5 corners (with possibly some or all of those corners being solved by chance). The possible cycle structures (ignoring directions of twists and with asterisks indicating a "misoriented cycle") are:

Code: 
{5}                1944
{3,1,1}             180
[b]{3,1*,1*}           360[/b]
{3*,1,1*}           720
[b]{3*,1*,1*}          360[/b]
{2,2,1}             135
[b]{2,2*,1*}           540[/b]
{2*,2*,1}           270
[b]{2*,2*,1*}          270[/b]
{1,1,1,1,1}           1 (cube solved)
{1,1,1,1*,1*}        20
{1,1,1*,1*,1*}       20
[b]{1,1*,1*,1*,1*}      30
{1*,1*,1*,1*,1*}     10[/b]

The numbers on the right are the number of cases (out of 4860) I calculated. So simply divide the number of cases by the total (4860) to get the probability of each case. The cases you specifically mentioned would correspond to {2,2*,1*} or {2*,2*,1*} which add to 810 cases, or 1/6 of all cases.

The cases in bold require at least three 3-cycles if solved only with 3-cycles. Of course, there are other ways these cases could be solved. You'll have to decide for yourself what you really mean when you say a case will "require three cycles" to solve. For example, the case {1*,1*,1*,1*,1*} requires four 3-cycles to solve with only 3-cycles, but could be solved with a 5-twist alg or two 5-cycles.
 
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cuBerBruce said:
okayama said:
cuBerBruce said:
Welcome to the "free insertion club," Tomoaki!

I call an insertion that doesn't increase the total number of moves of a solution as a free insertion.
Click to expand...

Wow thanks. Of course that was not intended, but just happened. :o
I'm curious about other membes of the club (and their insertion).

FYI, I once got a 9-moves cancellation at Weekly competition 2010-21.
Click to expand...
Wow! That was a "better than free" insertion in Weekly Comp 2010-21. I haven't followed the weekly comp much lately, so I wasn't aware that you were already in the free insertion club.

I'm not aware of anyone besides the two of us who are members of the free insertion club. My free insertion was in Fewest Moves Challenge #224, after which I started this thread in the Yahoo FMC group.
Click to expand...
I looked back the thread (Weekly Comp 2010-21) and found that Teemu Tiinanen had also done a free insertion (solution here). :)
There might be another member of the free insertion club.
 
I was pretty amazed when I saw those results yesterday!

Especially since I did not see any "undone" moves in the solutions, where all move so obvious?
Personally I have to move back and forth through my solution Alot and that is why I am not participating in the 10 min comp.

Will have a go at this scramble later today!
 
My 27-move solution from Helsinki Open 2011.

Scramble: L F2 L2 D2 R U2 R B2 R' B2 D2 F' D L2 D U2 F R D U' L
(Inverse scramble: L' U D' R' F' U2 D' L2 D' F D2 B2 R B2 R' U2 R' D2 L2 F2 L')

For the inverse scramble:
Double x-cross: B' U' B L D' R2 F' L F (9)
F2L minus slot: U' B'* U2 B (13)
Leave 3 corners: R' F' U' F U2 R (19)

I totally failed the insertion. I don't actually remember where I did it but it didn't cancel any moves. I just picked a random spot with 8 moves in time trouble, therefore 27 moves in total. I think I had about 18 minutes left when I started searching for the insertion, so I really should have found something. First time I went through the solution I found an insertion that was supposed to cancel 3 moves but it was wrong. :p Then I started to panic a bit and lost my focus, I still had to invert the solution in the end and I have some bad experiences debugging those for some reason. anyway after finishing I spent about 5 minutes on the insertion and easily found R D' R' U2 R D R' U2 at *, which cancels two moves. Probably one reason of failing was that the ink of my pen didn't stick to my stickers well, so it was easy to mess up the numbers in them. Another is of course that I haven't done much FMC lately. :p anyway I'm happy with another sub-30 solution :)
 
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Linear

F R U' D R' L' F D' R2 U2 R2 L2 D2 L' U' D2 L2 F' B R D L2 R2 B2 D'

B' U B2 F' R' B' D B2 F' R2 F B' (12/12)
L2 D L2 D L2 D2 L2 (7/19)
B R2 F' R' F R' B' D2 (8/27)

A little under 1min lolscramble is lol
 
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Scramble: D U F' D U' L2 F' R2 D2 R B' F L D R' F2 D2 U2 L B2 F2 D' L2 D B


Premoves: D L' D'

U B U' F' B2 L' D' L' U2 (double x-corss)
D2 B' D B R' D2 R D2 R (last 2 f2l couples)
[R] D R' D [R] ([R'] B' R F R' B R F') D2 R' (sune to fix edges + 2 moves canceling insertion)
D L' D' (premoves fixing)

33 HTM

I think that it's quite easy to find a better solution for the last 2 f2l couples... but I didn't :(
 
Well, I made that mostly for myself, and I already know all 6-9 movers, but in case someone wants it:


R U B U' B' R'
R U R' U R U2 R'
R U' L' U R' U' L
R B L' B L B2 R'
R U B' R B R' U' R'
R U R2 F R F2 U F
R U R' U' R' F R F'
R U R' F' L' U' L F
R U2 R' U2 R' F R F'
R B R' F R B' R' F'
R U B' U' R' U R B R'
R U2 R D R' U2 R D' R2
R U2 R D L' B2 L D' R2
R U2 R2 U' R2 U' R2 U2 R
R U2 R2 F R F' R U2 R'
R D2 L2 F U2 L2 D2 B R
R F' U2 F U2 F R2 F' R
R B2 R F2 R' B2 R F2 R2
R B2 L2 D L D' L B2 R'
R B' R F2 R' B R F2 R2
R B' R B2 L' B L B2 R2
R2 U F B' R2 F' B U R2
R2 F2 B2 L2 D R2 F2 B2 L2

(It's from a computer generated list I got from Teemu, that's why all algs begin with R.)
 
Good stuff, too bad I'm too lazy to learn a lot of algs...

BTW did you notice the similarity between Irontwigs and my solve in classic 331?
14 identical moves up to F2L minus one corner! Then it went downhill for me :(

http://fmc.mustcube.net/results.php?round=331&format=official&metric=htm

L F B' L R U F2 B' L U2 B2 F' U' B2 R2 D' U2 L2 U2 L2 R2 U' D2 F' R' F' L F U2 R

Irontwig
L' B':U B2 L2 B2 [2x2x2]
R' F R' D2 [XX-cross]
R2 U' R' U [F2L missing one corner]
B' R' D' R.D B R [Leaving five corners]
Insert at dot: R' D L D' R D L' D' (Six moves cancel)
Insert at colon: B' L' F' L B L' F L (One move cancel)

the novice:
L' B' U B2 L2 B2 2x2x2 + pair
R' F R' D2 2x2x3
R2 U' R' @ U F2L-corner
R D' F D F'R' F' R # F leaves 4 corners
# insert R' B' R F2 R' B R F2 to cancel 3 moves
@ insert B U' F U B' U' F' U to cancel 1 move
 
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Learning algs for FMC is imho way easier than for speed. E.g. I know 1/6-1/5 of ZBLL, but it feels like close to nothing to remember. I guess motivation helps a bit; I know that if I remember a LL alg in FMC I'll probably get a nice solve while in speed it's not too improbable for a newly learnt alg to make the time worse.
 
You got a point there, messing up an alg in FMC is not that bad, you can just try again ;-) or go ahead in the usual fashion.
I may actually look into some of these and see how they stick!
 
really short ones, if you get "lucky" and find a short solution for f2l and get an LL that looks like 6 move T + Y perm or Sune + U perm, from the right angles.
 
Relating to the OLL question above I have some questions for the experts:

What techniques / algs / methods do you think are most valuable for FMC?
Perhaps a preferred order in which to learn the various things would be usefull too?

Techniques I think can be usefull (in no particular order):
Blockbuilding Petrus
Blockbuilding Heise, I like Heise for the moment!
Knowledge of different methods ZZ, Petrus, Heise, CFOP, Keyhole, HTA
Pseudo blocks / premoves
Inverse scrambles
NISS
Corner / edge commutators for insertions
EO methods
Petrus
Heise (I still have to study the more advanced / combined last steps)
full PLL
full OLL (I use 2 look and know some dot / line cases)
LL algs (No knowledge whatsoever...)

Around EO I often take a quick look into which OLL I get without (or "half"...) EO and if OLL is not too bad I check the resulting PLL.
But unless it is a 6 move OLL followed by A or U perm I typically just do EO followed by whatever is needed.
For me this is often a Sune to fix EP and from there commutators for the remaining corners.

Perhaps I should make it a routine to check all OLL, you never know if it results in a PPL-skip.
Would it be worthwile to learn full OLL just for FMC? Or would I be better off studying the LL algs Irontwig posted recently?

Are there any other alg sets that may be of particular use?
 
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