2x2 scrambler programming project suggestion

[Kenneth]

I am not sure on the 11 move limit. I think if a scramble can be generated in N moves, it must also be generatable in N+M moves.

With exeptions, if you have a mix of quarter and half turns that is true, better to look at quarter turns, a scramble that is a uneven number of QTM must always have a uneven number. Take Niklas as an example, R' U L U' R U L' U' it is 8 QTM and optimal, all other algs that solves this case must have 8, 10, 12... QTM, newer 9, 11, 13...


Hey, look at that, it's my post #1,000

 

[qqwref]

That's obvious though Kenneth, and nobody generates scrambles in QTM...

Anyway I think that the assertion that "if a position can be solved in N moves HTM it can also be solved in N+M moves HTM" is not necessarily true. For example there is no way to solve the scramble U with two non-canceling moves. So unfortunately I think the assertion is not true in general and thus we might have to prove it somehow else.

Here is an interesting approach: suppose we have a scramble of k<11 moves, call it A B ... N. Then what we are actually looking for is a non-canceling 11+k move identity which starts with N' ... B' A'. That is - any 2x2 scramble can be solved in exactly 11 moves if and only if there is an 11+k move identity starting with every possible k-move scramble. So, if we could somehow find a way to list every 2x2 identity of 11+k moves, we could quite easily check to make sure that every possibility of the first k moves is accounted for. (Probabilistically speaking this is very likely, but we have to be sure...)

 

[Kenneth]

That's obvious though Kenneth, and nobody generates scrambles in QTM...

To you it is but not to anybody, you are not the only one who reads this forum

 

[qqwref]

You're right, maybe I'm overestimating the knowledge of theory on this forum. But still, I would expect all the people who are talking about math and theory (like Stefan, Bruce, you, Kociemba, TomZ, etc) to be well aware of that fact

 

[Kenneth]

Yes, true. But some that don't may like to learn, that's why I always try to explain as much as possible (sometimes it may look like I try to show off but I'm actually the mentor type, I like to see people learn things).

 

[AvGalen]

Interesting discussion, but why this fascination with exactly 11?

Scramblers are not supposed to solve those same scrambles.
Scramblers are not supposed to talk to competitors.
So what would be the problem if a scramble would be 10 moves (or 12?)

I would worry more about an 11 move scramble that has a 2 move solution.

 

[Stefan]

10 or 12? The blasphemy! Curse you Arnaud!

Having all scrambles the same length would be just *beautiful*. I agree 10 or 12 wouldn't really make a difference in practice, but... it wouldn't be beautiful. Something deep inside of me would cry and howl in pain. If it's possible to make it perfect, then I want it perfect.

The 2 move solution scramble and whether it's good is a different issue altogether. But compared to optimal length scrambles I'd prefer the 11 moves scrambles particularly for scrambles with short solutions. Two moves are probably trivial to spot anyway, but four aren't. And then it would be bad to see the scramblers picking up the cubes and putting them back after four moves. That would *tell* people that there's a short solution. And that's exactly what the idea discussed here tries to prevent.

 

[AvGalen]

10 or 12? The blasphemy! Curse you Arnaud!

Having all scrambles the same length would be just *beautiful*. I agree 10 or 12 wouldn't really make a difference in practice, but... it wouldn't be beautiful. Something deep inside of me would cry and howl in pain. If it's possible to make it perfect, then I want it perfect.

The 2 move solution scramble and whether it's good is a different issue altogether. But compared to optimal length scrambles I'd prefer the 11 moves scrambles particularly for scrambles with short solutions. Two moves are probably trivial to spot anyway, but four aren't. And then it would be bad to see the scramblers picking up the cubes and putting them back after four moves. That would *tell* people that there's a short solution. And that's exactly what the idea discussed here tries to prevent.

Oh, so the idea is to have beautiful scrambles. And beautiful means 11 moves always. Not 25 moves always and not an optimal scramble always. No, even if there is a 7 move scramble you want it transformed to an 11 move so you don't cry and howl in pain :rolleyes:

.................................................................OK, let's have someone else do it

 

[Stefan]

Don't obsess over the number 11. That's just because some cases require 11 moves, so a smaller number wouldn't always suffice. The real objective is not the number 11. The real objective is (A) having short scrambles so scrambling is fast and (B) not letting the scramble length give clues about the possible solution length. Having all scrambles the same length achieves (B) the best possible way, having them have 11 moves achieves (A) the best possible way (assuming all cases can indeed be generated in exactly 11 moves, which is still not clear).

 

[Stefan]

Scramblers are not supposed to solve those same scrambles.

Oh and this is actually wrong. As already mentioned in my initial post in this thread, this is not just intended for WCA competitions but also for private unofficial practice where we do scramble for ourselves.

 

[qqwref]

Can't we just switch to, say, 15 random moves for the time being? Even if we can't get optimal scrambles, 25 is way excessive.

If you don't like that, we could always just use 3x3 scrambles for official 2x2. It's faster to do 19 moves than 25 anyway...

 

[Stefan]

Well, Tomz' scrambler and Ron's latest reply in the WCA thread (http://www.worldcubeassociation.org/forum/viewtopic.php?p=2954#p2954) look promising.

 

[AvGalen]

Don't obsess over the number 11. That's just because some cases require 11 moves, so a smaller number wouldn't always suffice. The real objective is not the number 11. The real objective is (A) having short scrambles so scrambling is fast and (B) not letting the scramble length give clues about the possible solution length. Having all scrambles the same length achieves (B) the best possible way, having them have 11 moves achieves (A) the best possible way (assuming all cases can indeed be generated in exactly 11 moves, which is still not clear).

You know me well enough to know I understand where the 11 comes from. And you warning me about not obsessing about the number 11 sounds really weird after you said

I agree 10 or 12 wouldn't really make a difference in practice, but... it wouldn't be beautiful. Something deep inside of me would cry and howl in pain. If it's possible to make it perfect, then I want it perfect.

I like perfection, but I love simplicity. Simply providing a 15, 20 or even 25 moves scramble gives very random scrambles (some hard, some easy), is short enough for me and long enough for competitors that are looking at the scramblers.

I have some other requirements for good scrambles. If they are very short (like 11) I would just memo them while scrambling and might end up solving using the inverse scramble. (this has happened on clock-scrambles). I don't like those repetitive 45 FMC scrambles, but they prevent "inverse solving"