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Re: [LUG] Fwd: Speedy solution to Rubik's Cube

 

On Wed, Aug 11, 2010 at 3:42 PM, tom  wrote:
> Then again the it could be a cant see the wood for the trees problem - like
> Fermats last theorem - didnt fit in the margin of his notebook but I bet it
> didnt take up the 200 odd pages the prize winning solution gave.
> I think all you had to prove there was x**n is always less than x**(n+1)
> (for +ve  integer n and x) and that was that.

Erm.. no. It is generally assumed that Fermat was wrong when he
claimed to have a proof (one that didn't fit in the margin). Firstly
because despite over 300 years of efforts, no one has found a simple
proof of the theorem. Secondly, and foremostly, because Fermat was
wrong about at least one other thing he claimed to have proved. (And
there are relatively simple, but wrong, "proofs" known of the
theorem.) Assuming that Fermat did have a proof makes for a much
better story though.

> The rubics cube looks like there should be a sieve of eratosthenes type
> solution - theres only 4000 billion different states in 20 moves of rubic
> and if calculated using machine code thats only a couple of days on a modern
> pc

The actual number of different states is 43,252,003,274,489,856,000,
which is a factor 10 more than 4,000 billion and means it can't be
computed on a modern PC, or on any computer without using special
tricks: http://www.cube20.org/

(And yes, it was done using distributed computing.)

Martijn.

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