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Cube Exploring Competition : Kompetition 2

This competition got 4 contestants. Thank you for participation. This time the winner is not clear as there are some answers that I should probably consider wrong.

The first place goes either to @TipsterTrickster or @WoowyBaby.

The problems are the following:
@TipsterTrickster gave answer to 2A which had F2L -1 solved, so it already had 2x2x2 blocks solved so he should get 0 points for problem 2A. His solution was a 7-moved to a 2x2x2 on FR slot. So I think it wouldn't break the spirit of a competition if he could resubmit, but on the other hand I feel the rules were rather clear. Would love to hear what other contestants think about it.

In this case the winner should be @WoowyBaby, but he gave an amazing short 2.x answer to both generation problems (4.3 and 4.3A), but I'm not convinced if they are correct and he didn't reply to me in PM with any explaination how to use these sequences to actually solve any state. (Edit: he did now and his answer is actually correct!)
4.3: 2.03
(R z, y)
4.3A: 2.05
(R L', U F D)

I think it might be correct given, that I could come up with a complex 2.x solution to this problem.
The idea: OP-BLD style. We have one corner buffer and one edge buffer.

The idea is exactly the same for corners and edges.
1) We select one buffer piece and one target piece.
2) We come up with a sequence that cycles over all pieces except of a buffer
3) We use a swap algorithm that swaps buffer with target and we don't worry about orientation.
4) Swap algorithm also flips two edges that are neither target nor buffer so we can orientate pieces when they are all in their correct locations.


Alg1 SETUP = CORNER_SETUP EDGE_SETUP
Alg2 FLIP_AND_SWAP = JPERM + flip 2 corners + flip 2 edges = F' U' B2 U' L U' L' F U2 L2 U2 L2 B2 D' B2 D' R2 D2 R2 B2 R2


Where the exact algs are:
CORNER_SETUP = (F L D L D' F' R2 D L' D' L F L2 F' R2) //CORNER_SETUP
EDGE_SETUP = (U F2 U L2 B R2 U2 R2 B L2 D R2 U R2 L2 U2) //EDGE_SETUP

CORNER_SETUP is a 7-cycle, while EDGE_SETUP is 11-cycle so
EDGE_SETUP = (SETUP)56
CORNER_SETUP = (SETUP)22

flip(S,F) = (S2 F S2) (F S F' S' F' S F S' F S F S') (S2 F S2)'
We have two flipping algs (one for corners and one for edges):
flip(CORNER_SETUP, FLIP_AND_SWAP) = change orientation of a buffer and target corner
flip(EDGE_SETUP, FLIP_AND_SWAP) = change orientation of a buffer and target edge



To solve a cube you do 4 steps.
1) Permutate corners
2) Permutate edges
3) Orient corners and edges

1) Look what piece is in a buffer corner slot. Let's say that it's a piece X.

Call the CORNER_SETUP enough times so that the piece currently in X's spot is in target. Execute SWAP, Undo the setup.
Repeat until all Corners are in place.

2) Same but for edges.
Similar like in OP-BLD method every time we swap two edges we also swap two corners, but when all edges are in place all corners will be as well because parity.

3) Flip corners and edges.
Find a piece that has wrong orientation, bring it to the target location and execute flipping alg.

Cube Solved :)
F U2 L2 B2 F' U L2 U R2 D2 L' B L2 B' R2 U2

[(U F2 U L2 B R2 U2 R2 B L2 D R2 U R2 L2 U2)2: F' U' B2 U' L U' L' F U2 L2 U2 L2 B2 D' B2 D' R2 D2 R2 B2 R2]
[(U F2 U L2 B R2 U2 R2 B L2 D R2 U R2 L2 U2)6: F' U' B2 U' L U' L' F U2 L2 U2 L2 B2 D' B2 D' R2 D2 R2 B2 R2]
[(U F2 U L2 B R2 U2 R2 B L2 D R2 U R2 L2 U2)7: F' U' B2 U' L U' L' F U2 L2 U2 L2 B2 D' B2 D' R2 D2 R2 B2 R2]
[(U F2 U L2 B R2 U2 R2 B L2 D R2 U R2 L2 U2)3: F' U' B2 U' L U' L' F U2 L2 U2 L2 B2 D' B2 D' R2 D2 R2 B2 R2]
[(U F2 U L2 B R2 U2 R2 B L2 D R2 U R2 L2 U2)9: F' U' B2 U' L U' L' F U2 L2 U2 L2 B2 D' B2 D' R2 D2 R2 B2 R2]
[(U F2 U L2 B R2 U2 R2 B L2 D R2 U R2 L2 U2)1: F' U' B2 U' L U' L' F U2 L2 U2 L2 B2 D' B2 D' R2 D2 R2 B2 R2]
(F' U' B2 U' L U' L' F U2 L2 U2 L2 B2 D' B2 D' R2 D2 R2 B2 R2)
[(U F2 U L2 B R2 U2 R2 B L2 D R2 U R2 L2 U2)5: F' U' B2 U' L U' L' F U2 L2 U2 L2 B2 D' B2 D' R2 D2 R2 B2 R2]
[(U F2 U L2 B R2 U2 R2 B L2 D R2 U R2 L2 U2)10: F' U' B2 U' L U' L' F U2 L2 U2 L2 B2 D' B2 D' R2 D2 R2 B2 R2]

(F' U' B2 U' L U' L' F U2 L2 U2 L2 B2 D' B2 D' R2 D2 R2 B2 R2)

[(F L D L D' F' R2 D L' D' L F L2 F' R2)2: F' U' B2 U' L U' L' F U2 L2 U2 L2 B2 D' B2 D' R2 D2 R2 B2 R2]
[(F L D L D' F' R2 D L' D' L F L2 F' R2)3: F' U' B2 U' L U' L' F U2 L2 U2 L2 B2 D' B2 D' R2 D2 R2 B2 R2]
[(F L D L D' F' R2 D L' D' L F L2 F' R2)4: F' U' B2 U' L U' L' F U2 L2 U2 L2 B2 D' B2 D' R2 D2 R2 B2 R2]
[(F L D L D' F' R2 D L' D' L F L2 F' R2)6: F' U' B2 U' L U' L' F U2 L2 U2 L2 B2 D' B2 D' R2 D2 R2 B2 R2]
[(F L D L D' F' R2 D L' D' L F L2 F' R2)5: F' U' B2 U' L U' L' F U2 L2 U2 L2 B2 D' B2 D' R2 D2 R2 B2 R2]

//at this point all pieces are in place and we can do the flipping

Other interesting problem was recursion number. The recursion number of a sequence is a lowest common multiply(LCM) of the length of all cycles.
We can have 9 * 5 cycles of corners giving 45 as a perfect answer for a 2x2x2 cube and for edges we can additionally make a cycle of length 11 with an edge twist making the max recursion number 9 * 5 * 11 * 2 = 990.

Surprisingly some people have answered with Inifinity to a 1.INF problem getting painful 0 points. All nxnxn cubes have at most 24 pieces of one kind, so the recusion number can't be higher than LCM of (1,2,3,4,...24) which is 2^4 × 3^2 × 5 × 7 × 11 × 13 × 17 × 19 × 23 = 5354228880 and it can be squezzed on a 6x6x6. @TipsterTrickster was the closest with finding the optimal solution, but packed on a 7x7x7.

Other problems turned out to be rather easy.

So current standings are like this, but this is pending explanaition from @WoowyBaby about his solutions to the 4.X problems. If @TipsterTrickster will make a claim that the problem description was misleading and will like have his solution for 2A scored 7 and nobody objects I will probably accept it.

So the final standings might change.

Here are the final standings:

1. TipsterTrickster 867.00
2. WoowyBaby 790.32
3. brododragon 714.34
4. CuberStacke 692.01

Problem 1.3:
brododragon: answer: 315.0 score: 83.39835766034379
CuberStacke: answer: 210.0 score: 77.52009653651764
TipsterTrickster: answer: 990.0 score: 100.0
WoowyBaby: answer: 720.0 score: 95.38319290627571


Problem 1.2:
brododragon: answer: 36.0 score: 94.13807890996732
CuberStacke: answer: 30.0 score: 89.348540639004
TipsterTrickster: answer: 45.0 score: 100.0
WoowyBaby: answer: 45.0 score: 100.0


Problem 1.INF:
brododragon: answer: 2280.0 score: 37.799262300459965
CuberStacke: answer: 210.0 score: 26.140523935193762
TipsterTrickster: answer: 764889840.0 score: 100.0
WoowyBaby: answer: 720.0 score: 32.164132251914126


Problem 2A:
brododragon: answer: 7.0 score: 100.0
CuberStacke: answer: 7.0 score: 100.0
TipsterTrickster: answer: 7.0 score: 100.0
WoowyBaby: answer: 7.0 score: 100.0


Problem 2B:
brododragon: answer: 6.0 score: 100.0
CuberStacke: answer: 6.0 score: 100.0
TipsterTrickster: answer: 6.0 score: 100.0
WoowyBaby: answer: 6.0 score: 100.0


Problem 4.3:
brododragon: answer: 3.03 score: 67.00
CuberStacke: answer: 3.03 score: 67.00
TipsterTrickster: answer: 3.03 score: 67.00
WoowyBaby: answer: 2.03 score: 100.00


Problem 4.3A:
brododragon: answer: 5.05 score: 62.77
CuberStacke: answer: 5.05 score: 62.77
TipsterTrickster: answer: 3.17 score: 100.00
WoowyBaby: answer: 5.05 score: 62.77


Problem 5.B:
brododragon: answer: 13.0 score: 100.00
CuberStacke: answer: 13.0 score: 100.00
TipsterTrickster: answer: 13.0 score: 100.00
WoowyBaby: answer: 13.0 score: 100.00


Problem 5.B2:
brododragon: answer: 13.0 score: 69.23
CuberStacke: answer: 13.0 score: 69.23
TipsterTrickster: answer: 9.0 score: 100.00
WoowyBaby: answer: 9.0 score: 100.00

Edit: clarification from @WoowyBaby received.
Edit: As everyone agreed I gave TipsterTrickster 100 for 2A and WoowyBaby didn't provide a proof for his 4.3A answer so I gave him 50.5 there (I think it's fair to assume he would find that.
 
Last edited:
In these nemesis problems we only focus on 2x2x2 or cross on a D layer (yellow in WCA orientation).

2A) CFOP vs Petrus. Design a scramble that has a solved cross but has the toughest possible 2x2x2.
2B) Petrus vs CFOP. Design a scramble that has a solved 2x2x2, but has the toughest possible cross.

Score is a number of moves required to solve cross / 2x2x2. No need to find the shortest sequences
I guess it really doesn't say anything about other 2x2x2s being solved. I interpreted it to be that all yellow 2x2x2s had to be x moves to get a score of x but the rules actually aren't as clear as I thought they were...

EDIT: What was the 9-move solution to solve the B2?
 
EDIT: What was the 9-move solution to solve the B2?
R' L U2 F2 D2 R L' F2 U2 (9)
There are other solutions as well. (I believe 4 distinct)

Edit: Cube Explorer spits out this-
Searching depth 9

U D' R2 F2 L2 U' D F2 R2 (9f*)
U2 R2 L2 D2 F2 U2 R2 L2 D2 (9f*)
U2 R2 L2 D2 F2 D2 R2 L2 U2 (9f*)
U2 F2 R' L D2 F2 U2 R L' (9f*)
U' D L2 F2 R2 U D' F2 L2 (9f*)
R L' D2 F2 U2 R' L F2 D2 (9f*)
R2 U2 D2 L2 F2 R2 U2 D2 L2 (9f*)
R2 U2 D2 L2 F2 L2 U2 D2 R2 (9f*)
R2 F2 U D' L2 F2 R2 U' D (9f*)
R' L U2 F2 D2 R L' F2 U2 (9f*)
D2 R2 L2 U2 F2 U2 R2 L2 D2 (9f*)
D2 R2 L2 U2 F2 D2 R2 L2 U2 (9f*)
D2 F2 R L' U2 F2 D2 R' L (9f*)
L2 U2 D2 R2 F2 R2 U2 D2 L2 (9f*)
L2 U2 D2 R2 F2 L2 U2 D2 R2 (9f*)
L2 F2 U' D R2 F2 L2 U D' (9f*)
Searching depth 10
 
Edit: Cube Explorer spits out this-
Searching depth 9

U D' R2 F2 L2 U' D F2 R2 (9f*)
U2 R2 L2 D2 F2 U2 R2 L2 D2 (9f*)
U2 R2 L2 D2 F2 D2 R2 L2 U2 (9f*)
U2 F2 R' L D2 F2 U2 R L' (9f*)
U' D L2 F2 R2 U D' F2 L2 (9f*)
R L' D2 F2 U2 R' L F2 D2 (9f*)
R2 U2 D2 L2 F2 R2 U2 D2 L2 (9f*)
R2 U2 D2 L2 F2 L2 U2 D2 R2 (9f*)
R2 F2 U D' L2 F2 R2 U' D (9f*)
R' L U2 F2 D2 R L' F2 U2 (9f*)
D2 R2 L2 U2 F2 U2 R2 L2 D2 (9f*)
D2 R2 L2 U2 F2 D2 R2 L2 U2 (9f*)
D2 F2 R L' U2 F2 D2 R' L (9f*)
L2 U2 D2 R2 F2 R2 U2 D2 L2 (9f*)
L2 U2 D2 R2 F2 L2 U2 D2 R2 (9f*)
L2 F2 U' D R2 F2 L2 U D' (9f*)
Searching depth 10
I was literally about to reply with this hahaha. I'm surprised there are so many. That's really cool.
 
I resubmitted my solution as <my solution> y *4. I guess I misinterpreted the rules as "hardest possible hardest possible 2x2x2" so for example if there was a 3 move 2x2 but also a 7 move 2x2 the 7 move 2x2 would be the answer. I'm ok with whatever you guys decide and think is fair.
 
Ok. So after some discussions and considering what is fair I have made the following calls:
@TipsterTrickster gets 100 points for 2A
Those who anwered INF to 1.INF get points for the number they provided in 1.3 instead of 0 points.
@WoowyBaby gave the answer he can't prove for the 4.3A so I changed his answer to 5.05 everyone else gave as I think 0 points would be too harsh there.
After these updates here are the final standings.
100$ goes to @TipsterTrickster.

1. TipsterTrickster 867.00
2. WoowyBaby 790.32
3. brododragon 714.34
4. CuberStacke 692.01

In the meantime I'm working on the problems for another Kompetition which will be about other puzzles than 3x3. but I will try to think a little more about problems to maybe get a higher participation ;)
 
His solution is a very elegant one kind of similar to the solutions to 5.B
It's two center swap algorithms and U.
So e.g. R = move white center to the right face and do a U.
 
Awesome! Here are my solutions for anyone interested.
1.3: 990
D' L2 B' L' U2 B' D2 F R F R2 B U' B' D2
1.2: 45
U R' F R2 F' R D B2 D2
1.INF: 764889840
On a 7x7 5354228880/7 = 764889840
Number = number of pieces cycled
F = 2 pieces flipped, both being in separate cycles
T = 2 pieces twisted, both being in separate cycles, one twisted clockwise and the other counter clockwise.
vyYVpdHLYLE-QBG3hJIE1f0huSZJ3Ir4Rlur2E1eLXJLEzzH_vw9cfFc-LaHI9iz97TQITcWZ_qr-qPds25rys_s8_DrIKSNOEhKtFlrwPSYAONY063nx4iKUDCdeoagDtqzbJy6




2A: F R’ F’ R2 U’ R’ U2 F’ U’ F (7 move 222) later revised to: F R’ F’ R2 U’ R’ U2 F’ U’ F y F R’ F’ R2 U’ R’ U2 F’ U’ F y F R’ F’ R2 U’ R’ U2 F’ U’ F y F R’ F’ R2 U’ R’ U2 F’ U’ F y
2B: F R2 F U’ R’ U2 F R’ (6 move cross)


4.3: 3.03
(U, x, y)
4.3A: 3.17
(U, R L’ U D’ F’ B R L’, R L’ F’ B U’ D R L’)

5.B: 13
R’ L U2 D2 R’ L F’ R L’ U2 D2 R L’
5.B2: 9
U2 R2 L2 D2 F2 D2 R2 L2 U2
This was a lot of fun and I am super exited for the next one! Thank you for doing these.
 
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