Cube Exploring Competition : Kompetition 2

[kubesolver]

General

Second edition of my previous competition

The Kompetition starts now and will last until Monday 20th of April 13:00 Central Europe Summer Time. I reserve the right to finish it earlier if there is no new or updated submission nor a thread bump for more than 48 hours.

Prize for the winner 100$ cubicle gift card or similar.

Spoiler: Scoring

New scoring rules. For each problem where the higher the better your score is 100 * (your result) / (best result).In a problem where the lower is better we take do the reverse calculation so 100 * best result / your result.

For example:
In a problem 2 people got answers with a score of 8, 7, or 6 and once person gave incorrect answer.
The scores will be
8 => 100
7 => 100 * 7 / 8 = 87.56
6 => 100 * 6 / 8 = 75
wrong answer => 0

Spoiler: Problem Descriptions

Spoiler: Problem 1) Recursion number

Definition: Recursion Number (RN) of a sequence is the number of repetitions it takes to come back to starting position. E.g. R U R' U' has Recursion number 6 on nxnxn.

Design a sequence (or equivalent cube state) that has the highest RN.The answer sequence can be either in a regular notation or in some other description that tells how to construct this scramble. (e.g. you can draw the scrambled cube in paint or describe all stickers colors with some algorithm etc.) No rotations are allowed.

Note: You are expected to calculate the number yourself. I will only verify if it's correct if you're about to win a prize. If you miscalculate the number for your scramble it's considered incorrect answer and 0 points.

Score for each subproblem is a logarithm of a recursion number (no need to do FMC).

1.3) On a 3x3.
1.2) On a 2x2
1.Mega) REMOVED
1.INF) Infinite cube recursion:
What is the biggest possible number for any nxnxn cube? If you think it can be arbitrarily large please write Infinity.If it's not infinite please provide Score = sequence Recursion number / n (size of the cube),

Spoiler: Problem 2) Nemesis II

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

Spoiler: Problem 3) REMOVED

Removed

Spoiler: Problem 4) Generation

Definition generation: We will call a group of sequences a Cube-Generator if any scramble can be solved using only those sequences.

Spoiler: "examples"

Four sequences (A,B,C,D) is a Cube-Generator if any scramble can be solved with only A, B, C, D e.g. AABCCDABCDCBACDBADCABDCABD.
The most obvious Cube-Generator is (R,L,F,B,D,U).

Another popular example comes from the common "The cube can be solved by Jperms"
The solution to 4.3 could be
(JpermA, JpermB, x, y, z) for a score of 5.03 + 0.01 * 2 * Jperm

4.3) Design a smallest set of generators for the whole cube
4.3A) Design a smallest set of generators for the whole cube without allowing the use of rotations (only RLUFDB)

Score for each subproblem is the number of sequences + (total length of all sequences in HTM) / 100.
So for example the score for sequence (R2, x y U) is 2.04
If all your sequences are longer than 25 then your score is X.25 (so it's always better to come up with very complicated 3 sequences than 4 easy ones)

Spoiler: Problem 5) FMC

Solve the following scrambles with the fewest moves using only RLUDF moves. Score is the length of a sequence in HTM metric.
5.B) B
5.B2) B2

Spoiler: Submissions

Please post your submissions as a DM to me with a title Kompetition 2 and bump this thread.

Spoiler: Please send your answer in this exact format

1.3: 6
R U R' F'
1.2: 2
R2
1.INF: 11999191293921839123
Here is how to get it on 121x121x121 blablabla.

2A: R U R' U'
2B: R U R' U'

3: Removed

4.3: 5.05
(R, U, F, D, x)
4.3A: 5.07
(R, U, F, L, D x y)


5.B: 4
R F2 U R
5.B2: 4
R F2 R' U

Spoiler: mentions

Mentioning previous participatns
@WoowyBaby @CuberStache @xyzzy @GenTheThief @TipsterTrickster @brododragon

Edit: Generation problem slighlty changed (only subproblems 4.3 and 4.3A left).
Edit: Removed problem 3
Edit: Removed problem 1.MEGA
Edit: Added example for problem 4

 

[Cuberstache]

Wow, this looks so much more difficult than the last one! I can't wait to get started on it!

 

[Cubinwitdapizza]

Oh goodness, I want to compete but it’s so confusing for my tiny brain
I guess I’ll try, although some things will have to be explained to me more thoroughly.
EDIT: where’d all this money to give away come from lol

 

[Cubinwitdapizza]

Question, do I have to explain how I got the rn On the infinity problem?
And does the rn have to be 4 moves.

 

[kubesolver]

@Cubinwitdapizza Yes, you have to explain how to get your number.
Nothing has to be 4 moves.

Edit: I added a new subproblem 4.3A)

 

[Cuberstache]

Design a scramble with the highest possible God Number where ALL edges are oriented using the following definition:White edge is oriented if it's in the middle layer or if it's in the U or D layer and white sticker is attached to white center or yellow center. Similar for other colors.

I'm a bit confused by your definition of "oriented". A white edge in the middle layer is always oriented? What about edges that belong in the middle layer? Is this normal EO as in ZZ or is this a different definition?

 

[kubesolver]

Yes. According to the definition in a problem edges in the middle later are oriented.

 

[Cuberstache]

Yes. According to the definition in a problem edges in the middle later are oriented.

So if an edge is in the correct place in the middle layer, but flipped, it's considered oriented?

 

[kubesolver]

Ok. I think I said it wrong.
No edge is in the middle layer for BOTH of it's stickers. So the green-red edge is oriented if and only if
Green sticker touches Green or Blue center or Red sticker touches Red or Orange center.

 

[Deleted member 36445]

 

[kubesolver]

Actually the more I think about it. the more I dislike this problem so unless someone says that he already has spend a lot of time thinking about it I consider removing the problem "oriented god number" from a competition. There seems to be already a lot of work with other problems.

 

[Cuberstache]

Ok. I think I said it wrong.
No edge is in the middle layer for BOTH of it's stickers. So the green-red edge is oriented if and only if
Green sticker touches Green or Blue center or Red sticker touches Red or Orange center.

Thank you, this clarifies it. I understand the concept of EO just fine, it was just the way you explained it that made me unsure.

Actually the more I think about it. the more I dislike this problem so unless someone says that he already has spend a lot of time thinking about it I consider removing the problem "oriented god number" from a competition. There seems to be already a lot of work with other problems.

I would be ok with it being removed, but I now understand what the problem is asking.

 

[TipsterTrickster]

For question 1.2 should we only use RUF moves? because if you include BDL with that you can do a "rotation" with U D', F B', or R L'.

 

[ProStar]

Again, I'd do this but I can't get past the first problem without being confused lol

 

[Cuberstache]

Again, I'd do this but I can't get past the first problem without being confused lol

All you need to do is find a sequence of moves that, when repeated, gets the cube back to a solved state. The example given is the sexy move, R U R' U'. When you do that 6 times on a solved cube, it returns to the solved state. So that would be a score of 6. You want to get that number as high as possible. Something that eventually restores the cube to a solved state, but with as many repetitions as possible.

 

[brododragon]

4.3A) Design a smallest set of generators for the whole cube without allowing the use of rotations (only RLUFDB)

What about wide moves?

 

[kubesolver]

The problem 3) Oriented God Number has been removed.
The reasons are that now I think it's not that good of a problem and I underestimated how much work the other problems actually are so there is no need for more problems in this competition.

4.3A) What about wide moves?

Wide moves are forbidden. Only regular face turns R L U F D B are allowed.

For question 1.2 should we only use RUF moves? because if you include BDL with that you can do a "rotation" with U D', F B', or R L'.

RUF and BDL are both allowed in this case. But if the cube is solved in a wrong orientation it still counts as solved.

 

[WoowyBaby]

Bump! I'll start working on it now

 

[kubesolver]

Hi,

I have also removed the problem 1.MEGA.

I think there is more than enough to do in this comp and I will make another competition dedicated to non-cubic puzzle later.

 

[Cuberstache]

Hi,

I have also removed the problem 1.MEGA.

What? I spent like an hour on that and I came up with what I think is an amazingly clever solution. I can tell you my score if you want, I think you will be impressed.