How many solved positions for 3x3x3?

[yboy403]

I know the standard numbers are 43,252,003,274,489,856,000 possible configurations and 1 solved position. However, I was thinking about it and realized that if a cube was solved except for one move, that could basically be called a solved position, because most speedcubers could solve it in less than 0.1 seconds. Same goes for positions requiring two turns to solve, those aren't much harder.
Agree? Disagree? Is there any way to include those in the tally of "solved" positions? Please post.
(My first thread)

 

[koreancuber]

Would it be infinite? And one turn is not the solved position, it's one move from the solved position.

 

[dannyz0r]

1move +2

 

[TioMario]

WCA says solved is solved... period .
One turn from solved is +2

 

[iSpinz]

Because most speedcubers could solve it in less than 0.1 seconds.

Really?

 

[ianini]

I count 19. That's if R and R' as +'2 count as separate.

 

[mr. giggums]

Well if you consider a +2 a solved state then count the ways:
U U2 U' R R2 R' L L2 L' F F2 F' B B2 B' D D2 D'
Thats 18 plus the solve state so 19 in 43,252,003,274,489,856,000 would be considered solved.

 

[ianini]

^^ That's what I thought.

 

[DaijoCube]

I love mathematics <3

 

[Cyrus C.]

That was more like counting, not (tricky) mathematics.

 

[cmhardw]

Exactly 2 turns away from solved I count:

18*15 - 3*3*3 = 243

There are 18 possible first turns. After which there are 15 possible turns of a different layer (5 layers to choose from, and each layer has 3 ways to spin). However, this doubles counts all possible turns of two parallel layers. Considering any two parallel layers there are 3 ways to spin the first layer and 3 ways to spin the parallel layer. There are 3 sets of parallel layers, so 3*3*3 = 27 positions have been double counted.

So I guess you could say that counting the solved state, 1 move away from solved, and exactly 2 moves away from solved there are:

1 + 18 + 243 = 262 "solved" positions based on the first part of your question.

Chris

 

[miniGOINGS]

Because most speedcubers could solve it in less than 0.1 seconds.

Really?

My one move scramble for 2x2 was exactly 0.10.

 

[Cyrus C.]

What about 2 turns away? Most cubers can do 2 turns in less than .5 seconds.

 

[yboy403]

Because most speedcubers could solve it in less than 0.1 seconds.

Really?

hell, yeah. 0.1 seconds for a R move? Easy. If you can do a sune in 0.7, then work the rest out yourself.

 

[yboy403]

Exactly 2 turns away from solved I count:

18*15 - 3*3*3 = 243

There are 18 possible first turns. After which there are 15 possible turns of a different layer (5 layers to choose from, and each layer has 3 ways to spin). However, this doubles counts all possible turns of two parallel layers. Considering any two parallel layers there are 3 ways to spin the first layer and 3 ways to spin the parallel layer. There are 3 sets of parallel layers, so 3*3*3 = 27 positions have been double counted.

So I guess you could say that counting the solved state, 1 move away from solved, and exactly 2 moves away from solved there are:

1 + 18 + 243 = 262 "solved" positions based on the first part of your question.

Chris

doesn't have the same ring to it, does it?
"43 quadrillion possible positions, and only 262 solved positions"

 

[ben1996123]

I don't count 1 move away from solved as being solved.

My answer would have to be 2,048, due to centre rotations.

 

[yboy403]

Would it be infinite? And one turn is not the solved position, it's one move from the solved position.

1move +2

WCA says solved is solved... period .
One turn from solved is +2

I don't count 1 move away from solved as being solved.

My answer would have to be 2,048, due to centre rotations.

Interesting. anyway, this has nothing to do with speedcubing or the WCA, just cubing in general. What I'm saying is that when Rubik's prints on their packages, or Dan Harris writes on the back of his book (good book BTW), that the ratio of total positions to solved positions is 43,252,003,274,489,856,000:1, they're leaving out the fact that there are an unspecified number (ben1996123 says 2048, Chris says around 300) of positions that a person with no knowledge of Rubik's Cube could solve easily, and which most people (WCA aside) would not consider a scrambled state. And even the WCA acknowledges that one turn from solved is something, because they only give a penalty for it, not a DNF. All I want to know is, including up to three turns from solved, which is the maximum my 5-year-old sister has solved with no help, how many unstated "solved" positions are there besides the standard one with all sides the same colour. If you do come up with a number, I'd like to see how you got it, purely for educational purposes (my own)
Yerachmiel

 

[cuBerBruce]

I don't count 1 move away from solved as being solved.

My answer would have to be 2,048, due to centre rotations.

Good answer... except then the total number of configurations then has to be counted as 88580102706155225088000. This is really the correct number of (cubic) configurations of the pieces (assuming we don't care how the cube is oriented in space).

 

[DavidWoner]

1 move from solved is not solved. Period.

Because most speedcubers could solve it in less than 0.1 seconds.

Really?

hell, yeah. 0.1 seconds for a R move? Easy. If you can do a sune in 0.7, then work the rest out yourself.

You have to start and stop the timer.

 

[yboy403]

1 move from solved is not solved. Period.

Because most speedcubers could solve it in less than 0.1 seconds.

Really?

hell, yeah. 0.1 seconds for a R move? Easy. If you can do a sune in 0.7, then work the rest out yourself.

You have to start and stop the timer.

see his time for these cubes. Probably if you had to start and stop a timer it would be something similar. anyway, read my post two up from yours (above CuBerBruce). This really has nothing to do with speed, just difficulty. I just gave a rough estimate of the time needed to solve it (no timers involved) as an idea of how easy it is, and how it's more of a solved position than a scrambled one.
Yerachmiel