## Rubik's Cube Proof Cut To 25 Moves 386 386

KentuckyFC writes

*"A scrambled Rubik's cube can be solved in just 25 moves, regardless of the starting configuration. Tomas Rokicki, a Stanford-trained mathematician, has proven the new limit (down from 26 which was proved last year) using a neat piece of computer science. Rather than study individual moves, he's used the symmetry of the cube to study its transformations in sets. This allows him to separate the 'cube space' into 2 billion sets each containing 20 billion elements. He then shows that a large number of these sets are essentially equivalent to other sets and so can be ignored. Even then, to crunch through the remaining sets, he needed a workstation with 8GB of memory and around 1500 hours of time on a Q6600 CPU running at 1.6GHz. Next up, 24 moves."*
## 1.6ghz? (Score:4, Insightful)

## Theory versus practice (Score:5, Insightful)

This could make a good case study for business schools

## Re:Which 25 moves? (Score:5, Insightful)

In other words, they are left as an exercise to the reader.

## Re:Theory versus practice (Score:5, Insightful)

Instead, it makes a great case for doing the research on the front end to eliminate lengthy repetition of useless iterations to shorten the overall time.

## Re:Theory versus practice (Score:3, Insightful)

## Re:1.6ghz? (Score:3, Insightful)

Next up, videocards, ugh.

## Re:Which 25 moves? (Score:1, Insightful)

"for any starting position there exists a sequence of no more then 25 moves that will solve it"

it doesn't mean (among other things)

"there is a human usable method of solving a rubik's cube in 25 moves or less unassisted"

from TFA

"Where is this likely to finish? A number of configurations are known that can be solved in 20 moves"

Should read

"a number of configurations are known to have no solutions that are less then 20 moves"

whereas this

"it's also known that there are no configurations that can be solved in 21 moves."

I'm not even sure what they're trying to say here...

Is he trying to say that there is known to be no configurations for which the optimal solution is exactly 21 moves?

"What this problem is crying out for is a kindly set theorist who can prove exactly what the upper and lower limits should be without recourse to a few years of CPU time (although it may take a few years of brain time). Any takers?"

this sounds alot like "some real mathematician should prove this using non-bruteforce methods before these amatuers hurt themselves" which to me betrays a very shallow understanding of the problem coupled with a very condescending attitude

## Re:Which 25 moves? (Score:3, Insightful)

## Re:Wow, it really works (Score:5, Insightful)

## Re:You only need one (Score:4, Insightful)

## Re:Wow, it really works (Score:4, Insightful)

## Re:Which 25 moves? (Score:3, Insightful)

## Re:Which 25 moves? (Score:1, Insightful)

Unless they find a position that requires 25 moves to solve. End of argument.

## Re:Which 25 moves? (Score:5, Insightful)

Yup - that's a bizarre thing to say. Surely after the first move in solving a configuration that can be optimally solved in 22 moves you obtain a configuration that can be optimally solved in 21 moves, by definition?

## Re:Wow, it really works (Score:3, Insightful)

## Re:Wow, it really works (Score:3, Insightful)

## Re:Wow, it really works (Score:3, Insightful)