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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. -- The Mailing List for the Devon & Cornwall LUG http://mailman.dclug.org.uk/listinfo/list FAQ: http://www.dcglug.org.uk/listfaq