# Kube Exploring Kompetition (knowledge quiz with prizes)



## kubesolver (Mar 23, 2020)

The Kompetition:

I invite you to participate in a competition about exploring 3x3x3.

*General:*

There are several problems to solve. For each problem the scoring is as follows:
First place gets the most points, the second less etc. (100, 80, 70, 65, 60, 58, 56, 54, 52, 50, 49, ..., 1) or proportionally more for higher ranked problems.
If several people get the same score their points in this round are averaged (so if two people share first place they get 90 points each).

In all problems where you are asked to find a sequence then the shorter the better. HTM metric (no slice turns allowed) is used unless specified otherwise.

There are 9 100-points problems, 2-200 points problems and 3 500-points problems.

*Prizes: *

I will give out the cubicle vouchers or something similar. To begin with there is guaranteed 100$ for the winner.
I will add more prizes if there is a bigger interest in the comp. Those extra prizes will incentivize good results and early participation similar to my previous competition.

*Participation rules:*
- You can use a cube, pencil, paper etc.
- You CAN use alg.cubing.net or similar to visualize cube.
- You CANNOT use algdb or similar resources for prepared algorithms for various occasions.
- You CANNOT use cube explorer or similar program. Please be fair 
- If you want to win a money prize you have to share your WCA ID.
- When you have solved all problems please bump this thread  and send your answers to me in a Private Message with Title "Kompetition".
- It's ok to improve your solutions later, just bump the thread again and add your new answer to the Pivate Message.

Please only discuss clarity or validity of questions in this thread and not the solutions until the Kompetition is over.

Submissions will be accepted until the end of March (1.04.2020 0:01 CET that is european time zone).

Problems:


Spoiler



100 points problems:
10) Comm1: Find a sequence that swaps two edges and two corners (2c2e).
11) Comm2: Same but 3e
12) Comm3: Same but 3c
13) Comm4: same but 3c3e
14) Comm5: same but 4c4e
15) Odd Q: Is it possible to find a sequence that starts and ends in a solved position and has odd number of moves in QTM (only 90 degrees face turns, no slice moves).
15A) Odd Q2: Only if you answered Yes in previous question. Please write such a sequence.
16) RUF block Q: Is there any cube position that has 2x2x2 block solved, but that can't be solved with 3-gen?
16B) RUF block Q2: Only if you answered Yes in previous question. Please write a sequence leading to such a position.

200 points problems:
20) RU madness: for each of PLL algorithm groups: A, E, F, G, H, J, N, R, T, U, V, Y, Z
Can it be done with 2-gen (i.e. using 2 cube faces like R and U, excluding slices, rotations etc.) sequence? If yes please write the sequence.
Score / tie breakers: number of correct answers, number of yes answers, length of provided sequences.

21) LL Incompatibility: Find an OLL algorithm such that after some number of repetitions of this sequence the last layer is oriented, but not permuted correctly.

500 point problems:
50) Lotto: Guess the god number (HTM) for those scrambles:
Your result is the sum of differences between your answer and the right answer for each scramble. (the smaller difference the better)

1) B2 F2 D R2 D2 R2 F2 D' B2 U2 F2 U' B' U' L U2 F' R' B D' B L'
2) R2 D F2 D B2 L2 D' F2 L2 R2 U R2 U' B' R2 F R F' D L F D2
3) R' U' L' B2 U F' R U L U' F2 L2 U L2 U' R2 D F2 D R2 D L2
4) D2 R B2 R B2 F2 D2 F2 L B2 R' D2 U' R' D F' D R2 U B' F R2
5) L2 F2 R B2 D2 L2 U2 F2 R' U2 L' D L' R B F2 R' D' B
6) L' F2 D2 F2 D2 R D2 F2 L2 D2 L' B R2 F' R' D' U' B F' U F' R
7 L2 F L2 D2 B2 R2 B' D2 B U F2 L2 D R F2 D L' B F U'
8) F' U2 F' U2 F' U2 L2 F' D2 U2 R2 B' L2 F2 R' F2 U L' D' B2 U R U' R'
9) F2 R U2 R' B2 R B2 F2 U2 B2 R' D2 R B' R' F2 D U B D2 R2 D L2 F2 U' B2 U2 R2 U' L2 B'
10) R' U2 L F2 L' U2 R' D2 R F2 U2 R B L' U L2 R' F' U' R' F R2
11) R U2 B2 F D' U' D U R F D2 B F2
12) B2 U2 L2 R2 U' B2 U' F2 D' R2 F2 D2 U' F' L D2 F D' B2 R' U2 B
13) B2 L2 F2 U2 L2 F2 U2 F D2 F L B' R D' F' L' U R2 B D F
14) U2 R2 F2 U' R2 F2 B L D' R U2 B2 L2 F2 R2 U' F2 U L2 U' F2 D'

51) CFOP nemesis. Prepare a scramble that is as short as possible and has the hardest possible cross.
The better solution is the one with higher length of a shortest sequence to make cross of any color.
Tie breaker is second best cross .. etc. The last tie breaker is len of sequence.
52) Petrus nemesis. Prepare a scramble that is as short as possible and has the hardest possible 2x2x2 block.
Same scoring as in 51).




When submitting please use the following template:


Spoiler: Solutions template



10) R U R' U'
11) R U R' U'
12) R U R' U'
13) R U R' U'
14) R U R' U'
15) Yes
15A) R U R' U'
16) Yes
16B) R F U R' F U'
20.A) Yes R U R' U'
20.E) Yes R U R' U'
20.F) Yes R U R' U'
20.G) Yes R U R' U'
20.H) No
20.J) No
20.N) No
20.R) No
20.T) No
20.U) No
20.V) No
20.Y) No
20.Z) No
21) Yes R U R' U'
50.1) 21
50.2) 21
50.3) 21
50.4) 21
50.5) 21
50.6) 21
50.7) 21
50.8) 21
50.9) 21
50.10) 21
50.11) 21
50.12) 21
50.13) 21
50.14) 21
51) R U R' U'
52) R U R' U'


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## brododragon (Mar 23, 2020)

What if I don't have A WCA ID? Also, are x and z rotations allowed in the 2-gen problems?


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## WoowyBaby (Mar 23, 2020)

I have a question:
For problems 10) to 14), why is there “Comm#” before the question?
Do you want the answers to be a commutator or something? Or are you just looking for the shortest sequence that fulfills that goal?

Also just a side note, the problems where you guess the god’s number is basically just luck lol.

Anyway, I’m really excited to do this! 
Sounds fun!!


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## kubesolver (Mar 23, 2020)

brododragon said:


> What if I don't have A WCA ID?


Then if you win you'll have to wait until your first competition to claim the prize.


brododragon said:


> Also, are x and z rotations allowed in the 2-gen problems?


no. 


WoowyBaby said:


> why is there “Comm#” before the question?


it's just the name of a problem so that you don't always have to refer to them by number.


WoowyBaby said:


> Or are you just looking for the shortest sequence that fulfills that goal?


Yes.



> Do you want the answers to be a commutator or something?
> Also just a side note, the problems where you guess the god’s number is basically just luck lol.


This is borderline crossing the "please don't discuss questions".


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## brododragon (Mar 23, 2020)

kubesolver said:


> Then if you win you'll have to wait until your first competition to claim the prize.
> 
> lol, no.
> 
> ...


Thank you for clearing things up!

Edit: One more thing: Can we use fractions/decimals for answers for GN questions?

Edit 2: Do we have to do Ua and Ub perms?


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## Cuberstache (Mar 23, 2020)

Do 10-14 have to be in HTM or are slice moves allowed?

Also, thanks for doing this! It's really interesting!


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## WoowyBaby (Mar 23, 2020)

kubesolver said:


> it's just the name of a problem so that you don't always have to refer to them by number.
> 
> Yes.


Thank you for your response 


kubesolver said:


> This is borderline crossing the "please don't discuss questions".



I’m sorry. I hope I am not already disqualified for that and I’ll be sure to be more careful.


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## Cuberstache (Mar 23, 2020)

Alright, done. I think I did pretty well. I sent you a PM, like you said.

EDIT: For #14, does it have to be a continuous cycle of 4 edges and 4 corners, or does 2e2e2c2c count?


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## kubesolver (Mar 23, 2020)

brododragon said:


> Edit: One more thing: Can we use fractions/decimals for answers for GN questions?


Yes.



brododragon said:


> Edit 2: Do we have to do Ua and Ub perms?


No, just one is enough (obviously if one can be than the other can as well)


CuberStache said:


> Do 10-14 have to be in HTM or are slice moves allowed?


I think HTM, but I'm open to change this rule if people prefer it.



WoowyBaby said:


> I’m sorry. I hope I am not already disqualified for that and I’ll be sure to be more careful.


No worries. My goal is to encourage people and have fun so I won't be disqualifying anyone for such minor things.



CuberStache said:


> For #14, does it have to be a continuous cycle of 4 edges and 4 corners, or does 2e2e2c2c count?


It has co be continuous. 2c2c is not the same as 4c.

Edit: I also made some small edits to the rules. In particular scoring of the Nemesis problems and some minor clarifications.


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## TipsterTrickster (Mar 23, 2020)

Bump!
Yay another competition by you! Your last one was a lot of fun and so far this one has been very fun too!


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## xyzzy (Mar 24, 2020)

kubesolver said:


> Can it be done with 2-gen (e.g. RU) sequence? If yes please write the sequence.


Does the "2-gen" have to specifically be ⟨R, U⟩?


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## kubesolver (Mar 24, 2020)

xyzzy said:


> Does the "2-gen" have to specifically be ⟨R, U⟩?


No, but good luck solving anything with (R,L)


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## brododragon (Mar 24, 2020)

kubesolver said:


> No, but good luck solving anything with (R,L)


Could you use slice moves?


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## kubesolver (Mar 24, 2020)

brododragon said:


> Could you use slice moves?


No, only face turns can be used.


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## WoowyBaby (Mar 24, 2020)

Bump! I'm finished with all of the problems and submitted my results!

I will probably try to improve 51 and 52 later and resubmit sometime before March 31.

This competition has been very fun and enjoyable!


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## GenTheThief (Mar 24, 2020)

For problem 21, should number of repetitions be considered?
If I have two algs, one taking 14 moves and 6 repetitions to reach an oriented yet non permuted state, and another taking 16 moves and 2 repetitions to reach such a state, which would receive the most amount of points?


E: Regardless, I've submitted my solutions. I can change it later if I come up with something better.


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## xyzzy (Mar 24, 2020)

Piggybacking on the above question:
Is the alg allowed to start/end with U moves? Is the alg allowed to include rotations?

Does being a U/U'/U2 off count as being permuted correctly, or as being permuted incorrectly?


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## kubesolver (Mar 24, 2020)

GenTheThief said:


> For problem 21, should number of repetitions be considered?
> If I have two algs, one taking 14 moves and 6 repetitions to reach an oriented yet non permuted state, and another taking 16 moves and 2 repetitions to reach such a state, which would receive the most amount of points?


The 14 moves sequence is shorter and is better. The number of repetitions required to achieve the state desired LL incompatibility doesn't matter.


xyzzy said:


> Piggybacking on the above question:
> Is the alg allowed to start/end with U moves? Is the alg allowed to include rotations?


Yes, the alg can include whatever.


xyzzy said:


> Does being a U/U'/U2 off count as being permuted correctly, or as being permuted incorrectly?


Let's assume for the purpose of this problem that it's correctly permuted.


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## kubesolver (Mar 27, 2020)

Shamelessly bumping my thread before the weekend.


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## brododragon (Mar 28, 2020)

I guess I'll submit it. Not the greatest, but an attempt.


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## kubesolver (Mar 31, 2020)

I'm pleased to anounce the results of a Kompetition.



Spoiler



Thank you to all who participated. Thank you, thank you, thank you, thank you, thank you, thank you 
Even if I hoped for a bigger participation I am still very happy with the quality of the submitted entries.



Spoiler



As expected the winner was decided in the last 3 500-point problems. Two contenders for the first place gave equally good answers to all except for the 500 points problems.
Most competitors gave very similar quality answers for all 100 points problems.



Spoiler



Let's look into some more interesting problems from the competition.



Spoiler



LL incompatibility:
Most competitoris came up with a regular cross case OLL "R U2 R2 U R2 U R2 U2", but xxyzzy come up with something very creative and claimed 200 for this problem with 7-mover "y2 L' U R U' L U R" while all other major competitors presented 9 move solutions.



Spoiler



CFOP / petrus nemesis:

Both problems had an answer scramble which required 8 moves to solve any cross or Petrus block respectively. The answer was not surprisingly some variation of super-flip.
Two people (Tipster and General) found 8 move solution for a CFOP nemesis with Tipster Trickster showing the shorter solution. WOW baby was the only one to find a 8 move scramble for Petrus Nemesis.

At this point Tipster Trickster had a very slight lead over WOW Baby because of his short 7-move Petrus Nemesis. But the margin between those two was very tiny and Lotto was meant to be decisive problem.



Spoiler



The deciding scrambles were 7 and 14 which had god number 12 and 14 respectively.
Tipster gave them both 18 while WOW Baby guessed 12 for both scrambles.



Spoiler: And the winner is 



WOW Baby is the winner of a Kompetition. By claiming (4th, 1st, 1st) places in 500 points problems he got just a tiny bit ahead of Tipster who got (1st, 2nd, 2nd).
xxyzzy was in the lead after 200 points problems and came third by claiming 3x 3rd place in 500 point problems.

Congrats! I present the solutions of a winner in case I missed something. If there are no protests I will be shipping winning prize to the WoW baby 



Spoiler: god numbers for Lotto



1) B2 F2 D R2 D2 R2 F2 D' B2 U2 F2 U' B' U' L U2 F' R' B D' B L' (18)
2) R2 D F2 D B2 L2 D' F2 L2 R2 U R2 U' B' R2 F R F' D L F D2 (20)
3) R' U' L' B2 U F' R U L U' F2 L2 U L2 U' R2 D F2 D R2 D L2 (14)
4) D2 R B2 R B2 F2 D2 F2 L B2 R' D2 U' R' D F' D R2 U B' F R2 (16)
5) L2 F2 R B2 D2 L2 U2 F2 R' U2 L' D L' R B F2 R' D' B (17)
6) L' F2 D2 F2 D2 R D2 F2 L2 D2 L' B R2 F' R' D' U' B F' U F' R (19)
7) L2 F L2 D2 B2 R2 B' D2 B U F2 L2 D R F2 D L' B F U' (12)
8) F' U2 F' U2 F' U2 L2 F' D2 U2 R2 B' L2 F2 R' F2 U L' D' B2 U R U' R' (13)
9) F2 R U2 R' B2 R B2 F2 U2 B2 R' D2 R B' R' F2 D U B D2 R2 D L2 F2 U' B2 U2 R2 U' L2 B' (6)
10) R' U2 L F2 L' U2 R' D2 R F2 U2 R B L' U L2 R' F' U' R' F R2 (17)
11) R U2 B2 F D' U' D U R F D2 B F2 (9)
12) B2 U2 L2 R2 U' B2 U' F2 D' R2 F2 D2 U' F' L D2 F D' B2 R' U2 B (15)
13) B2 L2 F2 U2 L2 F2 U2 F D2 F L B' R D' F' L' U R2 B D F (20)
14) U2 R2 F2 U' R2 F2 B L D' R U2 B2 L2 F2 R2 U' F2 U L2 U' F2 D' (14)





Spoiler: Solutions of a winner



10) R F' R U2 L' B L U2 R2 F
11) D B2 U D' R2 U'
12) F2 U B U' F2 U B' U'
13) R F2 L' F2 L F2 R' F2
14) U
15) No
16) No
20.A) No
20.E) No
20.F) No
20.G) No
20.H) Yes, R2 U2 R U2 R2 U2 R2 U2 R U2 R2
20.J) No
20.N) No
20.R) No
20.T) No
20.U) Yes, R2 U R U R' U' R' U' R' U R'
20.V) No
20.Y) No
20.Z) Yes, R2 U R2 U R U2 R2 U2 R2 U2 R U' R2 U' R2
21) U L F R' F' L' F R F'
50.1) 18
50.2) 17
50.3) 17
50.4) 17
50.5) 18
50.6) 18
50.7) 12
50.8) 12
50.9) 6
50.10) 17
50.11) 9
50.12) 17
50.13) 18
50.14) 12
51) B R L F U' D' B D' L F2 U2 L2 U' R2 U' D L2 U' R2 D2 R2 U2 L U F2 U' F2 U' D2 B2 D
52) B R F D' L' U' B R' U2 L' U2 L' B2 U2 F2 D' R2 D' L2 D L2 D' F' B U R2 F2 B2 L2 D' F' B


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## ProStar (Mar 31, 2020)

Congrats @WoowyBaby!


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## fun at the joy (Mar 31, 2020)

kubesolver said:


> Submissions will be accepted until the end of March (1.04.2020 0:01 CET that is european time zone).


?
I haven't submitted because it is still 31st March. 

Congrats to @WoowyBaby to win this awesome competition!


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## brododragon (Mar 31, 2020)

Can you release a complete leaderboard @kubesolver?


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## TipsterTrickster (Mar 31, 2020)

Dang nice job @WoowyBaby! I pretty much just guessed 18 for most of the scrambles, and then tried finding easy solutions for the easy looking scrambles lol.


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## Cuberstache (Apr 1, 2020)

Yeah, in hindsight, guessing that it was 17 or 18 for everything was a bad strategy given that a human picked the scrambles. It should have been obvious that it wasn't going to be a normal distribution.


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## WoowyBaby (Apr 1, 2020)

Wooaaahhhh what??? There’s no way I won!

I was not expecting this!! 

@xxyzzy Nice job finding a 7 move solution to the LL Compatibility problem! I totally forgot about rotations so I got 9 moves but I could have gotten lower if I used rotations, because, like yours, mine was actually just a 3 corner commutator but without/plus a move; but oh well the competition is over too late now haha.
Good job on that one @xxyzzy !! 

Hmmm, I seem to have failed the CFOP nemesis problem?? That confuses me... My sequence brought it to the Checkerboard + Superflip state which is symmetrical and 8 moves for every cross, but I guess I messed up in writing down my solution down or something? Darn, I maybe I should’ve doubled checked that one. I’m a bit disappointed in myself.
Too late now, I suppose.
I’ll be okay with 4th place on that one.

I like how am I referred to as “WOW baby”. It makes me laugh xd. It’s WoowyBaby, but I find it pretty silly so I don’t mind.
‘WOW baby found this and WOW baby did this’ Haha, funny 

@CuberStache you’re right about not normal optimal distribution, that is what I realized once I noticed that one of the scrambles could just be reduced down to 9 just by removing moves. I now treated this set as completely picked out by a human.
Then, I found the 6 move optimal solution on one of the scrambles, and in total I believe I found 3 or so of the optimals by hand. I was tempted to just guess 17 or 18 for the rest of them, so I did for the most part, but put in 12 for a couple just because I knew that it was a human chosen set so some will be unusually low, and I got very very lucky with those.

For the final two, CFOP nemesis and Petrus nemesis, I was totally going to resubmit a much short solution for getting to those states.
I did a super quick FMC of like 5 minutes each so I had sequences of 31 and 32 moves, but from what I read it actually did not matter in the end if I FMC-ed them further to 25 moves, or even 20.

That was a big risk I made, but I’m glad it didn’t cost me in the end. 

@kubesolver Thank you for hosting this amazing online Kompetition!
I found it very new and exciting and I really appreciate the effort you put into making this!
Even if there was no prize it would definitely still be a great experience (But I’m not saying I don't appreciate this prize, I really do)

Thank you so much for this wonderful Kompetition!


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## Cuberstache (Apr 1, 2020)

WoowyBaby said:


> @CuberStache you’re right about not normal optimal distribution, that is what I realized once I noticed that one of the scrambles could just be reduced down to 9 just by removing moves. I now treated this set as completely picked out by a human.
> Then, I found the 6 move optimal solution on one of the scrambles, and in total I believe I found 3 or so of the optimals by hand. I was tempted to just guess 17 or 18 for the rest of them, so I did for the most part, but put in 12 for a couple just because I knew that it was a human chosen set so some will be unusually low, and I got very very lucky with those.


I didn't find the 6-move solution lol I felt so dumb


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## xyzzy (Apr 1, 2020)

TipsterTrickster said:


> Dang nice job @WoowyBaby! I pretty much just guessed 18 for most of the scrambles, and then tried finding easy solutions for the easy looking scrambles lol.





CuberStache said:


> Yeah, in hindsight, guessing that it was 17 or 18 for everything was a bad strategy given that a human picked the scrambles. It should have been obvious that it wasn't going to be a normal distribution.


Oh same, I guessed 17 for most of them, but I also guessed 16 for two of them (#8 and #10) because those had easy-looking blocks lol. (Just in case, I also did linear FMC solves on all of the scrambles, but besides the 6-mover and the 9-mover, they were all in the 30-45 range which obviously is way too large.)


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## kubesolver (Apr 1, 2020)

@WoowyBaby I promise I won't mistype your name. I'm sorry I was lazy and didn't do this correction in the text.
Those who participated. Which kind of problems would you like to see more in the future Kompetition 2?


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## brododragon (Apr 1, 2020)

kubesolver said:


> @WoowyBaby I promise I won't mistype your name. I'm sorry I was lazy and didn't do this correction in the text.
> Those who participated. Which kind of problems would you like to see more in the future Kompetition 2?


No GN questions and more questions like 21 where it's not too difficult, but still very complex.


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## WoowyBaby (Apr 1, 2020)

There is a Kompetition #2 that's going to happen?? That's super exciting!


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## Cuberstache (Apr 1, 2020)

Maybe some stuff on puzzles other than 3x3? I actually would like some more GN problems though, to redeem myself haha.


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## kubesolver (Apr 1, 2020)

It's not easy to come up with questions like 21. This single question was going on my head for some time and was the inspiration to do this comp.
I'll try to be creative.


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## TipsterTrickster (Apr 1, 2020)

Yeah, I would love to see other puzzles involved! This was so much fun and I’m super hyped that your thinking about doing another one!


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## ProStar (Apr 1, 2020)

I saw it, was like "this will be fun!", looked at the first question, and gave up


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## Cuberstache (Apr 1, 2020)

ProStar said:


> I saw it, was like "this will be fun!", looked at the first question, and gave up


Quite a few PLLs swap two edges and two corners. You could have done a T-perm, for example. I used the shorter Ja perm for mine.


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## brododragon (Apr 1, 2020)

CuberStache said:


> Quite a few PLLs swap two edges and two corners. You could have done a T-perm, for example. I used the shorter Ja perm for mine.


Wait.. don't commutators have to be x y x' y'?


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## Cuberstache (Apr 1, 2020)

brododragon said:


> Wait.. don't commutators have to be x y x' y'?


The use of the word "commutator" in this particular question is a bit misleading


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## xcross (Apr 19, 2020)

Problem 20 is impossible, isnt it? For a 2gen LL to exist the corners must all be permuted, if they aren't than it is impossible to solve with only 2 gen.


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## brododragon (Apr 19, 2020)

xcross said:


> Problem 20 is impossible, isnt it? For a 2gen LL to exist the corners must all be permuted, if they aren't than it is impossible to solve with only 2 gen.


You just got points for as many as you could find, as some are in fact impossible look at the submissions template.


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