Author: J. Wesley Cleveland
Date: 11:55:59 12/12/02
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On December 12, 2002 at 14:08:22, Dann Corbit wrote: >On December 12, 2002 at 12:47:20, J. Wesley Cleveland wrote: >[snip] >>You are the one that said you could prove that chess was not currently solvable, >>which means others can speculate and you have to prove them wrong. > >I was wrong. See some other message I wrote elsewhere in this thread in answer >to Heiner. >[snip] >>The proof takes only a few steps. Define king confined in a rectangle n,m as >>queen on square n+1,m+1, king in the rectangle not adjacent to the queen, and >>opposing king outside the rectangle n+1,m+1. Prove if the king is confined in a >>rectangle of 3,1 or 3,2, it is checkmate. Prove if the king is confined in a >>rectangle of n,1, you can force it to be confined in a rectangle of n-1,1. Prove >>if the king is confined in a rectangle of n,m, you can force it to be confined >>in a rectangle of n-1,m or n,m-1. Prove that you can confine the king in a >>rectangle. QED. > >This proof will take exactly the same number of steps to complete as the tree >search. Hence it is an implicit tree. > >I could just post a ten line minimax algorithm and say: >"Chess is solved." > >We can easily show that the algorithm terminates. Do you not understand (or remember (or accept ;)) the concept of "proof by induction" ? My algorithm can find a move that will lead to mate from any starting position (with the side with the queen to move) with at most a 5 ply search (I am pretty sure that it could be done with no search, but hesitate to say I can prove it). I do not know of any such algorithm for chess ;), but cannot prove it does not exist.
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