2-move solves

[Dane man]

Woah, what happened here? Well, I'd say no. A sub 1 WR would be fun, but also kinda.... I dunno, I'd put myself on a guilt trip 'cus it'd feel like cheating even if it wasn't.

But that sub-1 WR would be very, VERY tempting... I'm not sure 15 seconds is enough to decide. I think instinct would kick in and I'd get a sub 1 just because it's there... then I'd feel bad forever.. or at least unless they discounted it our had someone else beat it for real. ;P

Maybe they'll change the rule to require at least 6 moves on 3x3 (so that intuiting a direct solution isn't all that simple).

 

[Bunyanderman]

The real question is how many two move solutions can come from a 25 move scramble?

 

[goodatthis]

The real question is how many two move solutions can come from a 25 move scramble?

The scramble length doesn't matter, if it's a random state scramble, then 243. Approximately 1/167 quadrillion of all possible combinations. I posted it on the last page, along with some interesting statistics

 

[Bunyanderman]

The scramble length doesn't matter, if it's a random state scramble, then 243. Approximately 1/167 quadrillion of all possible combinations. I posted it on the last page, along with some interesting statistics

Thank for the reply, but doesn't answer my question. I would think that a 25 move scramble has a lower chance to have a 2-move solution that a 100 move scramble.

 

[Julian]

Thank for the reply, but doesn't answer my question. I would think that a 25 move scramble has a lower chance to have a 2-move solution that a 100 move scramble.

Random-state means that a position of the ~43 quintillion available is chosen at random. Then a scramble is generated which will give the chosen position. Each position has an equal chance of being chosen. Like goodatthis said, the scramble length doesn't matter.

 

[Bunyanderman]

Random-state means that a position of the ~43 quintillion available is chosen at random. Then a scramble is generated which will give the chosen position. Each position has an equal chance of being chosen. Like goodatthis said, the scramble length doesn't matter.

I think we are all confused (probably me more,) yes I get that now, but is it more likely to have a 2-move solution out of 25 random moves, or more than that (100 moves?)

 

[guysensei1]

Hmm, doesn't the random state scrambler generate optimal (or near optimal) scrambles? So a 2 move state would have a 2 move scramble right?

 

[Julian]

Hmm, doesn't the random state scrambler generate optimal (or near optimal) scrambles? So a 2 move state would have a 2 move scramble right?

They can be told to generate optimal or sub-optimal scrambles.

 

[DeeDubb]

I think we are all confused (probably me more,) yes I get that now, but is it more likely to have a 2-move solution out of 25 random moves, or more than that (100 moves?)

After you get past a certain point, it becomes pretty much the same likelyhood. 100 moves, 1000 moves, 10000 moves, all have the same chance of having any given random state, including the 2 move solution. 20 moves might be SLIGHTLY more likely because it is under God's number for 3x3, but I don't really know for sure.

 

[elrog]

After you get past a certain point, it becomes pretty much the same likelyhood. 100 moves, 1000 moves, 10000 moves, all have the same chance of having any given random state, including the 2 move solution. 20 moves might be SLIGHTLY more likely because it is under God's number for 3x3, but I don't really know for sure.

I would like to clarify something in your post. You said that X moves have the same chance to give a random state, but some states are more likely to occur than others due to symmetries. On a supercube, every state has equal probability. I think what you were meaning though is that X moves and Y moves both have the same chance to come up with the same state.

Lets say you start at any particular random state on the cube. If you apply exactly 20 moves to the cube, there may be cases that are still unreachable. Take a state that is 19 moves optimally from the state you started at. That state is only reachable if it is solvable in 20 moves as well as the optimal 19 moves. I am fairly certain that there are 19 move optimal solutions that cannot be solved in exactly 20 moves because there are also 5 move solutions which cannot be solved in 6 moves.

It is true that the probability would eventually be the same, but to define the point, you would have to find a number big enough that every state can be solved in exactly that many moves. There may also be a few numbers of moves above this number of moves which cannot cover every position, but it seems that eventually you would reach a point where any number of moves above this number, whatever it may be, would be able to cover every position. I cannot be to sure though as prime numbers would seem the same way, but they really only become further and further apart.


Oh, and to answer the original question disregarding the point that the chances are so small, I have not and may not ever attend a competition, and that the scramble would surely be thrown out, I would solve the cube in 1 move STM if possible and give up if it wasn't possible.

 

[goodatthis]

I think we are all confused (probably me more,) yes I get that now, but is it more likely to have a 2-move solution out of 25 random moves, or more than that (100 moves?)

Basically the way it works is a computer program randomly picks a position, (out of 43 quintillion, 243 is the amount that are 2 moves away) let's just say it's the checkerboard pattern. Then the computer tries to solve that position, and yields a solution, which would be something like R2 L2 U2 D2 F2 B2. After that, the computer inverts the solution to instead of solving a given position, it turns a solved cube into that given position, and that's what a scramble is. Move length of the scramble has nothing to do with it when we are talking about random state scramblers.

Does that answer your question? Since Gods Number is 20, if you scramble a cube with 20 moves, and that scramble is sure to yield a random state, (not just random moves) anything over 20 moves is completely useless and wastes moves. Therefore, if you had a random state scrambler (random moves scramblers aren't used anymore) that was really inefficient and gave 100 move solutions to given positions, it wouldn't matter. Because it's the position on the cube that matters, not the moves being done to it.