Random Cubing Discussion

A review from The Cubicle's 13x13 page:

When I received this package at my doorstep, I couldn't believe the size of it. I am not one for working out to often, so I knew that there was no way I could lift the package into my home. After hours of intense thinking and planning, I decided that the most efficient way of transporting this package into my house was not to bring the package to my house; but bring my house to my package! It was genius! I arranged a few guys to come over and demolish my home. But don't worry we rebuilt it a few inches over so that the package had a roof covering it. But the challenges were still not over... I had to find a way to open the package that contained the moyu 13x13. All of my knifes were in the dish washer. Then I remembered I had 20 sharp objects, my teeth! I fast as I could I bit around the package. The swallowed and spit out cardboard. Then I saw it... The 13x13 laid right in front of my eyes. My heart raced and pounded against my chest. Little did I know but in the next 3 seconds I was to pass out! Minutes past by until I woke up. This was it, now was the time I would turn the moyu 13x13! I lined my hands up against the edges of the cube. My muscles vibrated as I readied myself. The soft layers of the cube turned with ease and I squealed with joy! After seconds of playing the puzzle popped! I didn't feel like putting it back together, so I just threw it away. Overall I really enjoyed my time with the moyu 13x13 and I think you should get it.

I found it pretty funny.
 
A review from The Cubicle's 13x13 page:

When I received this package at my doorstep, I couldn't believe the size of it. I am not one for working out to often, so I knew that there was no way I could lift the package into my home. After hours of intense thinking and planning, I decided that the most efficient way of transporting this package into my house was not to bring the package to my house; but bring my house to my package! It was genius! I arranged a few guys to come over and demolish my home. But don't worry we rebuilt it a few inches over so that the package had a roof covering it. But the challenges were still not over... I had to find a way to open the package that contained the moyu 13x13. All of my knifes were in the dish washer. Then I remembered I had 20 sharp objects, my teeth! I fast as I could I bit around the package. The swallowed and spit out cardboard. Then I saw it... The 13x13 laid right in front of my eyes. My heart raced and pounded against my chest. Little did I know but in the next 3 seconds I was to pass out! Minutes past by until I woke up. This was it, now was the time I would turn the moyu 13x13! I lined my hands up against the edges of the cube. My muscles vibrated as I readied myself. The soft layers of the cube turned with ease and I squealed with joy! After seconds of playing the puzzle popped! I didn't feel like putting it back together, so I just threw it away. Overall I really enjoyed my time with the moyu 13x13 and I think you should get it.

I found it pretty funny.

I don't understand the meaning of this review (my english isn't very good). Is he exaggerating the fact that it's a very big cube and inventing a fake story about that ? (In this case, i would admit that it's a bit funny too.)
 
What's the shortest algorithm that can affect (unsolve?) 4 corners pure? Doesn't matter where they are or how the 4 corners are affected. Can be a 2-2 swap or a 4 corner twist or 1 corner twisted and a 3 cycle.

What's the shortest for 5 corners?

X perm can be done in 10 moves which is move optimal afaik... http://alg.cubing.net/?alg=F2_L2_R2_B2_D_B2_R2_L2_F2_U

That X-perm alg is indeed optimal, and there are no cases for 4 bad corners in less than 10 moves. So 10 is minimal for 4 bad corners.

The only "n bad corners" cases (n > 0) less than 10 moves are corner 3-cycles and this 6 bad corners case (and symmetrical equivalences):

(U2 R2 F2)3
 
Assuming the cubecomps results are correct, IranFMC 2015 is a very silly competition.

14 competitors - of which 6 (43%) got no successful solves at all. In fact, 64% of solves were DNF or DNS. The best three solves were 29, 30, 32 - but those cubers did not get means. Nobody else got a solve under 37 moves. Actually, only two people (14%) got a mean, and the winning mean was 52.33 moves, which is roughly the same as a high-end CFOP speedsolve.

Pretty bad... but not quite as bad as Java FMC Cube Day 2010 :p
 
Assuming the cubecomps results are correct, IranFMC 2015 is a very silly competition.

14 competitors - of which 6 (43%) got no successful solves at all. In fact, 64% of solves were DNF or DNS. The best three solves were 29, 30, 32 - but those cubers did not get means. Nobody else got a solve under 37 moves. Actually, only two people (14%) got a mean, and the winning mean was 52.33 moves, which is roughly the same as a high-end CFOP speedsolve.

Pretty bad... but not quite as bad as Java FMC Cube Day 2010 :p

Wasn't there this one other comp where almost everyone had a DNF average for 3x3?
 
What's the shortest for 5 corners?

I believe I have solved all symmetrically distinct pure 5 bad corners cases in Cube Explorer. The minimal move count is 10. All 10-move cases are 5-cycles.

U2 F U2 R2 D2 L2 B L2 D2 R2 (10f*)
F' U2 F U2 L' U2 F' U2 F L (10f*)
F R' U2 R U2 F' U2 R' U2 R (10f*)
U F2 R' F2 U' F2 U R U' F2 (10f*)
B U B' L2 B L2 U' L2 B' L2 (10f*)
F2 U2 L F2 L' U2 F2 L' U2 L (10f*)
F U2 R2 D2 L2 B L2 D2 R2 U2 (10f*)
L' B2 U2 L' B2 L U2 B2 L U2 (10f*)
F2 R' F2 U' F2 R F2 R' U R (10f*)
L2 U' B U L2 U' L2 B' L2 U (10f*)
U L2 U' B U L2 U' L2 B' L2 (10f*)
L2 B L2 U L2 U' B' U L2 U' (10f*)
R2 F' R2 F U' F' R2 F R2 U (10f*)
U F2 R F2 R' U' R F2 R' F2 (10f*)
U' R2 F' R2 U R2 U' F U R2 (10f*)
R2 U' F' U R2 U' R2 F R2 U (10f*)
F2 D R2 D' F2 R2 D' F2 D R2 (10f*)
F2 R' F2 U F2 R F2 R' U' R (10f*)
F U' F' R2 F R2 U R2 F' R2 (10f*)
L2 B2 U' B2 L2 F2 R2 D' R2 F2 (10f*)
R2 D R2 B' R2 B D' B' R2 B (10f*)
R2 F' R2 F U F' R2 F R2 U' (10f*)
B U2 L' U2 L B' L' U2 L U2 (10f*)
B U2 B' L' B U2 B' U2 L U2 (10f*)

Incidentally, the worst case optimal move count was 17. These are pure 5-twist cases.
R' F2 U R U' L2 B2 U' B2 U B2 L2 R' F2 U R U' (17f*)
U' L2 R D2 B2 L' D2 F L' F' R2 U2 F' R' F' R2 U' (17f*)

EDIT:
I now believe I have solved all symmetrically distinct cases for 4 bad corners with Cube Explorer. The minimal cases are all double swaps:

F2 D B2 L2 D' F2 U B2 R2 U' (10f*)
R2 F2 D L2 D' F2 R2 U B2 U' (10f*)
R2 B D2 B' R2 U2 F L2 F' U2 (10f*)
L2 R2 D2 F' D2 L2 R2 U2 B' U2 (10f*)
R' D2 B2 F2 U2 L' D2 B2 F2 U2 (10f*)

The worst case is 16 moves. All 16-move cases are pure twists.

F' U2 F U2 F2 R' D' F' L F2 L' D R U' F' U' (16f*)
R F2 U' L' R' D L R U F2 R' D U L' D' U' (16f*)
U' R B L2 F' U2 R2 F R' D2 R' U2 F L2 R' U' (16f*)
 
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