Author: Dann Corbit
Date: 15:54:33 12/10/02
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On December 10, 2002 at 18:44:55, Ingo Lindam wrote: >On December 10, 2002 at 18:30:42, Dann Corbit wrote: > >>If I have a king and a rook verses a king, I can store a perfect solution to the >>puzzle in a tree. I can use only sqrt(n) possible states to form the solution >>and the solution will be optimal. You may find another solution, but it will >>not be superior to mine in any way. > >Dann, >I am sure I can proof KR vs. K is won just using a pencil and a single sheet of >paper... > >do I get the fields price for that? Will it be a proof for an aribitrary position? Or a proof for an individual position? An example is *NOT* a proof. In order to *prove* something you must show that there are *ZERO* exceptions. Now, with a king, a rook and an opponent king, there are less than: 64*63*62 possible positions (many of them being illegal positions). The total is therefore less than 249984 and the square root of that is 500. Will you provide a formal proof with less than 500 pieces of information in total that shows it will work for every conceivable board state? I know you are thinking of an algorithmic solution. But if you follow the algorithm, you will see that it forms a tree. From here: [D]8/8/2K5/R7/4k3/8/8/8 b - - The black king can move to: [D]8/8/2K5/R7/3k4/8/8/8 b - - [D]8/8/2K5/R7/8/3k4/8/8 b - - [D]8/8/2K5/R7/8/4k3/8/8 b - - [D]8/8/2K5/R7/8/5k2/8/8 b - - [D]8/8/2K5/R7/5k2/8/8/8 b - - You will need to provide a response to each one of these. It continues forward to solution. The moves are obvious, but what we are encoding is the tree. The optimal move will form the minimal tree, if we make it each time. We could use a tablebase, but to *form* the tablebase, we must have formed the search beforehand.
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