Author: Ingo Lindam
Date: 16:16:06 12/10/02
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On December 10, 2002 at 18:54:33, Dann Corbit wrote: >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. But we don't need to show the shortest win to mate to show that we will mate the black king by using a given algorithm. Ingo
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