# [WCA Regulations 2012] Clock Notation



## Lucas Garron (Dec 13, 2011)

We need a good notation for the official Clock scrambler.

Ideally, it would have the following properties:

 Easy for a cuber to learn, and to pick up if they don't know it / have forgotten. Ideally, even if they don't know much about clock (even how the pegs connect to dials).
 Not annoying for a fast cuber.
 Ideally, a single string that can fit on one line.

Existing ideas:


WCA 2010 Official

```
UU  u=-2
dd  d=3

dU  u=0
dU  d=-5
```

qqtimer

```
UU u2'   dU
dd d3    dU d5'
```

Clément's Proposal:
(UUdd, -2, 3) (dUdU, 0, -5)


Combining qqtimer and Clément's:
(UUdd, U2', d3) (dUdU, U0, d5')
or
(UUdd, U2' d3) (dUdU, d5')

Issues:

 Does "UUdd" suggest UF-UR-DL-DR or could it be suggesting going clockwise UL-UR-DR-DL to anyone?
 From Sébastien: Does U2', d3 suggest turning the clocks attached to pegs pegs pressed "Up " and "down", or does it suggest turning the the top and botom clocks? (I think this is pretty clear, given a peg arrangement like "UUdd".)
 Could "(ddUU, -2, 3)" be interpreted as turning "d2' U3" instead of "U2' d3"?
 Is it even a good idea to use "d" and "U" to distinguish pegs as up and down?


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## Stefan (Dec 14, 2011)

I don't have a full suggestion, but I'd like to mention that we don't have to use "down-pin turns". Just like when solving, we could scramble using only "up-pin turns" by flipping the clock. A partial scramble could look like

U4 R2' D1' L6 A3 flip U2' R3 D3' L5 A4'

where for example U4 means having the upper two pins up and turning one of the upper two wheels four hours clockwise. "A" means "all". The above partial scramble does 10 of the usual 14 turns, so a full scramble wouldn't be much longer. I think of them as scrambling centers and edges, I'm just not entirely sure about how to do the corners.

Edit: could use "y2" instead of "flip" to prevent x2-flipping and to stay closer to cube-notation


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## Sebastien (Dec 14, 2011)

Lucas Garron said:


> Could "(ddUU, -2, 3)" be interpreted as turning "d2' U3" instead of "U2' d3"?


 
This corresponds more to my point than the one you mention above that one 

This makes 90% of my clock scrambling mistakes btw. And I would consider myself as a quite experienced clock scrambler.

I want to state another of my point:

Clock differs a lot from cubid puzzlers and due to my competition experience Clock scrambling is always very dependant from experienced Clock solvers. So to my mind your first point



Lucas Garron said:


> Easy for a cuber to learn, and to pick up if they don't know it / have forgotten. Ideally, even if they don't know much about clock (even how the pegs connect to dials).


 
is rather irrelevant.


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## Stefan (Dec 14, 2011)

Stefan said:


> I'm just not entirely sure about how to do the corners.



I suspect this would work, but I'm not sure it doesn't create unwanted dependencies:

U4 R2' D1' L6 A3 flip U2' R3 D3' L5 A4' UL3 UR4' DR6 DL4

*(Edit: *UL means having the UL pin up and turning the UL wheel. Intended "for the corners".*)*

The order can also be changed, these might be better for pin adjustment:

U4 R2' D1' L6 A3 flip UR3 DR4' DL6 UL4 U2' R3 D3' L5 A4'
UR3 DR4' DL6 UL4 U4 R2' D1' L6 A3 flip U2' R3 D3' L5 A4'

And here's a variation that uses +/- instead of the optional apostrophe. Might improve spacing/readability.

U4+ R2- D1- L6+ A3+ y2 U2- R3+ D3- L5+ A4- UL3+ UR4- DR6+ DL4+


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## Sebastien (Dec 14, 2011)

Well Stefan, you already once revolutionized scrambling for Megaminx and I would like if you find a similar way for clock as well. 

Using {UL, UR, DL DR}-Notation makes a lot of sense to me btw. This would satisfy Lucas proposals as well I think. Also flips would not be needed.


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## Stefan (Dec 14, 2011)

Sébastien_Auroux said:


> Well Stefan, you already once revolutionized scrambling for Megaminx and I would like if you find a similar way for clock as well.



I already like my scramble style, but I could use the help of some math guy to prove that the chosen 14 turns are independent (or to find nice 14 independent turns).



Sébastien_Auroux said:


> {UL, UR, DL DR}-Notation


 
Which one is that?
(In case you meant my previous post, you probably misunderstood me... I've added a clarification now)



Sébastien_Auroux said:


> Also flips would not be needed.



How?


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## qqwref (Dec 14, 2011)

Lucas Garron said:


> [*]Combining qqtimer and Clément's:
> (UUdd, U2' d3) (dUdU, d5')


I like this one. The only real issue is, as you said below, the 4 letters being possibly interpreted as being clockwise rather than left-to-right.

I do think "U" and "d" are not entirely clear, but I'm not sure if we can do better - we'll always have to explain something like "turn one of the corners next to an up peg". For the pictures of pegs we could use O and . for up and down; we could also use pictures like Jaap's pictoral clock scrambler.

I am actually pretty strongly against any "non-verbose" notation, such as (-2,3) (4,6) etc, or the notation Stefan said below (U4 R2' D1'). The reason is that it's just too unintuitive - you basically have to memorize the order of steps and what to do. So this kind of thing is only acceptable for people who do hundreds of clock solves, and unfortunately the scramblers are often not these people. In fact, I've had scramblers and judges who basically had to be told what was turnable and what the solved position was. Whatever we choose absolutely needs to be very intuitive and clear.


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## Stefan (Dec 14, 2011)

qqwref said:


> I am actually pretty strongly against any "non-verbose" notation, such as (-2,3) (4,6) etc, or the notation Stefan said below (U4 R2' D1'). The reason is that it's just too unintuitive - you basically *have to memorize the order of steps* and what to do.


 
Huh? No, it's explicitly written right there. Just read it left to right and apply the moves:

U4: With U pins up, turn U wheels 4 hours clockwise
R2': With R pins up, turn R wheels 2 hours counterclockwise
D1': With D pins up, turn D wheels 1 hour counterclockwise
...

This is no less verbose than for example (UUdd, U2' d3) (dUdU, d5'). Quite the contrary, for *that one* you need to memorize an order (of the pins for the "UUdd"). I actually find mine much easier and clearer.


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## Zarxrax (Dec 14, 2011)

Simple suggestion...
Notation is complex because everything is in corners.
If we simply turn the whole clock at a 45 degree angle, then it simply becomes U, D, L, R

Uppercase letters can refer to wheels, and lowercase to pins.


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## Stefan (Dec 14, 2011)

Zarxrax said:


> If we simply turn the whole clock at a 45 degree angle, then it simply becomes U, D, L, R



What moves do you envision with that?
How might a complete scramble look like?


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## StachuK1992 (Dec 14, 2011)

I'd say


r U2 l D3 r'
would mean
right peg in, turn top twice, left peg in, turn down 3 times, right peg out.


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## Zarxrax (Dec 14, 2011)

Yes, like that.


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## Sebastien (Dec 14, 2011)

Stefan said:


> Which one is that?
> (In case you meant my previous post, you probably misunderstood me... I've added a clarification now)


 
Well, indipendently of understanding what you mean or not:

Clarifying which wheel to turn (UL, UR, DL, DR) instead of just demanding "turn a wheel where a pin is uo/down" would clarify a lot of stuff.


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## Lucas Garron (Dec 14, 2011)

Sébastien_Auroux said:


> Clock differs a lot from cubid puzzlers and due to my competition experience Clock scrambling is always very dependant from experienced Clock solvers. So to my mind your first point is rather irrelevant.


I don't think it should have to be that way. If we could find a notation that wasn't too hard for a common cuber to learn and read correctly, that would be good, right? 





Stefan said:


> U4+ R2- D1- L6+ A3+ y2 U2- R3+ D3- L5+ A4- UL3+ UR4- DR6+ DL4+


I think this is the best I've seen so far. Someone care to make a pretty diagrams that has 9 images in a line showing clearly how do execute each move?




StachuK1992 said:


> r U2 l D3 r'
> would mean
> right peg in, turn top twice, left peg in, turn down 3 times, right peg out.


- First of all, tilting is going to be arbitrary and unintuitive.
- Distinguishing the meanings of the letters is going to be hard.
- It's easier to get lost because you have to follow a specific sequence of peg changes, instead of being able to read exactly how the pegs should be right now.


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## StachuK1992 (Dec 14, 2011)

Lucas Garron said:


> - First of all, tilting is going to be arbitrary and unintuitive.
> - Distinguishing the meanings of the letters is going to be hard.
> - It's easier to get lost because you have to follow a specific sequence of peg changes, instead of being able to read exactly how the pegs should be right now.


-does that matter? Is holding green front and white top not unintuitive, and arbitrary at the least?
-I don't see how.
-that's the best argument against this. At the very least, I think Zarxrax's idea should be kept in consideration.


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## Stefan (Dec 14, 2011)

Lucas Garron said:


> Someone care to make a pretty diagrams that has 9 images in a line showing clearly how do execute each move?



Let's first find out whether this scrambling is actually valid (that the 14 turns are independent and can create all possible puzzle states).



Lucas Garron said:


> - It's easier to get lost because you have to follow a specific sequence of peg changes, instead of being able to read exactly how the pegs should be right now.


 
Well, instead of peg changes, the lower case letters could describe peg states. Like r meaning r up (and no others), and ru meaning r and u up (and no others).


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## Stefan (Dec 14, 2011)

Stefan said:


> Let's first find out whether this scrambling is actually valid (that the 14 turns are independent and can create all possible puzzle states).


 
I just entered

1 1 1 1 1 1 1 1 1 
1 1 0 1 1 0 0 0 0 
0 1 1 0 1 1 0 0 0 
0 0 0 1 1 0 1 1 0 
0 0 0 0 1 1 0 1 1 
1 1 1 1 1 1 0 0 0 
0 0 0 1 1 1 1 1 1 
1 1 0 1 1 0 1 1 0 
0 1 1 0 1 1 0 1 1 
(each row is a move, telling which clocks it affects)

into http://www.bluebit.gr/matrix-calculator/ and let it compute Matrix Rank. It said it's 9. Am I right that that's a proof? (It's just for one side, but the other side's cross is clearly independent)


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## Lucas Garron (Dec 14, 2011)

Stefan said:


> Am I right that that's a proof? (It's just for one side, but the other side's cross is clearly independent)


Probably. You could also try to find algs to turn any single dial using only those turns (basically only three needed; A is also unneeded).


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## Stefan (Dec 14, 2011)

Lucas Garron said:


> You could also try to find algs to turn any single dial using only those turns



Ok, I just did, that works. Using my notation (omitting "1" everywhere):

Center: A U' D' L' R' UL UR DL DR
Edge: UL UR U' and then fix the center with the above
Corner: UL and then fix center and edges with the above



Lucas Garron said:


> A is also unneeded



What do you mean?

"A" is my only up-pin turn allowing an overall odd hours change. Without it, I'd need a diagonal turn, a down-pin turn, or an up-pin turn on the other side affecting the parity on this side. I dislike the first two and I'm too tired right now to think about the third 

I'd like to find seven up-pin moves with which I can turn any single dial on one side except two corners. Then the same moves could be used for the other side, that would be neat.


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## clement (Jan 4, 2012)

Stefan said:


> U4+ R2- D1- L6+ A3+ y2 U2- R3+ D3- L5+ A4- UL3+ UR4- DR6+ DL4+


I'm a little late. I like this proposal. Here is an alternative without flipping the clock :
U4+ d3- R2- l3+ D1- u2- L6+ r5+ UL3+ UR4- DR6+ DL4+ A3+ a4-
This is closer to the actual order of scrambling. upper-case: pins up, lower-case: pins dows.


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## Lucas Garron (Jan 4, 2012)

clement said:


> I'm a little late. I like this proposal. Here is an alternative without flipping the clock :
> U4+ d3- R2- l3+ D1- u2- L6+ r5+ UL3+ UR4- DR6+ DL4+ A3+ a4-
> This is closer to the actual order of scrambling. upper-case: pins up, lower-case: pins dows.



I think the lowercase letters prevent it from being as easy to understand as possible.

B the way, Mark 2 currently uses:

```
[UUdd] U4 d2' [dUdU] U5 d5 [ddUU] U2' d5' [UdUd] U4' d5 [dUUU] U3' [UdUU] U3 [UUUd] U3 [UUdU] U3 [UUUU] U5 [dddd] d2' [ddUd]
```
This does't deal with peg order, nor with clarifying what U4 or d2' mean, but I think it's actually quite readable.


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## ben1996123 (Jan 4, 2012)

```
UU   dU   dd   Ud   dU   Ud   UU   UU   UU   dd   Ud
dd   dU   UU   Ud   UU   UU   Ud   dU   UU   dd   dd

u=-2 --   u=2  u=-4 u=2  u=-4 u=5  u=-1 u=2  --   --
d=3  d=-5 d=-1 d=6  --   --   --   --   --   d=-3 --
```

I would prefer something like this. Easily understandable.


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## Pedro (Feb 9, 2012)

I talked to Lucas yesterday, and came up with this: http://www.cuber.com.br/clockScrambler.html

It uses Clément's idea (UUdd,1,2)...

Suggestions are welcome.


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## Pedro (Feb 9, 2012)

Shameless bump, but I did some improvement.

Printing the page will now only show the image and competition name/round, which the user can input.

Here's a sample: http://www.cuber.com.br/clockScramble.pdf


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## Mike Hughey (Feb 9, 2012)

I feel like someone should respond to this - it looks like a lot of work and a nice job, so I think someone should say something.

It looks very pretty!

I have to admit, I personally find the pictures with each step to be rather distracting - I'd rather just have the text and maybe the final picture. But at the same time, I know that it is often true that you have the need for non-clock-solvers to scramble clock, and for them, the step-by-step pictures for the pins and directions seem rather nice. And I suspect it would actually be pretty easy to ignore the pictures once you got into scrambling. So I think that overall this seems like a really big improvement to me. I like it - I hope something like this will be adopted.


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## Mollerz (Feb 9, 2012)

Mike Hughey said:


> I feel like someone should respond to this - it looks like a lot of work and a nice job, so I think someone should say something.
> 
> It looks very pretty!
> 
> I have to admit, I personally find the pictures with each step to be rather distracting - I'd rather just have the text and maybe the final picture. But at the same time, I know that it is often true that you have the need for non-clock-solvers to scramble clock, and for them, the step-by-step pictures for the pins and directions seem rather nice. And I suspect it would actually be pretty easy to ignore the pictures once you got into scrambling. So I think that overall this seems like a really big improvement to me. I like it - I hope something like this will be adopted.


 
I think this is good because there are pictures to aid those who don't know how to scramble for when needed in competition, but those who know the pin order can just use the numbers underneath to scramble fast.

I like it a lot.


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## Mike Hughey (Feb 9, 2012)

Oh, I just realized one thing: I think you should definitely have a text representation of the pin configuration at the end. Sometimes diagrams don't print properly, and the delegate might occasionally not notice a problem with it. If the pin configuration is in text, you won't get in trouble if, for instance, the printer leaves doubt as to the difference between yellow and brown in the diagram. And anyway, I think it's important to have a scramble that is expressed entirely in text.


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## MaeLSTRoM (Feb 9, 2012)

Just me or are the numbers on the diagram wrong for all the UdUU moves?
Apart from that, looks good. Maybe 2 contrasting colours for pin up/down?


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## Pedro (Feb 9, 2012)

Yttrium said:


> I think this is good because there are pictures to aid those who don't know how to scramble for when needed in competition, but those who know the pin order can just use the numbers underneath to scramble fast.
> 
> I like it a lot.


Yes, that's the idea. I can scramble fine just reading the text below the images. You can filter them out if you want to.



Mike Hughey said:


> Oh, I just realized one thing: I think you should definitely have a text representation of the pin configuration at the end. Sometimes diagrams don't print properly, and the delegate might occasionally not notice a problem with it. If the pin configuration is in text, you won't get in trouble if, for instance, the printer leaves doubt as to the difference between yellow and brown in the diagram. And anyway, I think it's important to have a scramble that is expressed entirely in text.


Added. The complete scrambles are at the textarea below (which doesn't get printed)



MaeLSTRoM said:


> Just me or are the numbers on the diagram wrong for all the UdUU moves?
> Apart from that, looks good. Maybe 2 contrasting colours for pin up/down?


You were right. That's what Ctrl+C Ctrl+V can cause  Fixed now.

You guys should also post at the WCA forum here: https://worldcubeassociation.org/forum/viewtopic.php?f=4&t=948


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## Mike Hughey (Feb 9, 2012)

Pedro said:


> Added. The complete scrambles are at the textarea below (which doesn't get printed)


Can you update the printed version (pdf)? The printed version is the one that most people will care about for bringing to competitions, so it's what I'm most interested in seeing corrected.


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## Pedro (Feb 9, 2012)

Sure. http://www.cuber.com.br/clockScramble.pdf


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## bamilan (Feb 9, 2012)

Is it possible to reorder the scrambling order? (just exchange the 2nd and 3rd ones) So we should not need so many clock rotations.
Scrambling position is with the clocks looking to the left, then after 2nd scramlbling step we would do an F on the whole puzzle, and finish scrambling as usual.
Using that you can use only the top wheels, which is more comfortable and a bit faster.


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## Pedro (Feb 9, 2012)

bamilan said:


> Is it possible to reorder the scrambling order? (just exchange the 2nd and 3rd ones) So we should not need so many clock rotations.
> Scrambling position is with the clocks looking to the left, then after 2nd scramlbling step we would do an F on the whole puzzle, and finish scrambling as usual.
> Using that you can use only the top wheels, which is more comfortable and a bit faster.


I don't know. I just did a visual representation of the current scramble. You should post on the wca forum (https://worldcubeassociation.org/forum/viewtopic.php?f=4&t=948) about that. I agree it would make it easier.


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