Author: Uri Blass
Date: 09:00:08 02/11/01
Go up one level in this thread
On February 11, 2001 at 10:39:26, Heiner Marxen wrote: >On February 11, 2001 at 08:33:11, Tim Foden wrote: > >>On February 11, 2001 at 00:29:23, Uri Blass wrote: >> >>>On February 10, 2001 at 16:26:39, Pete Galati wrote: >>> >>>>This is another position that crashes Crafty, so I assume that the Chessbase >>>>interfaces probably won't like it either. >>> >>>The chessbase interface have different rules then crafty. >>> >>>It does not like positions when >>>max(number of white bishops-2,0)+max(number of white knights-2,0)+max(number of >>>white rooks-2,0)+max(number of white queens-1,0)+number of white pawns>8 >>> >>>It also does not like cases when it is truth for black and does not like >>>positions with more or less than one king for one of the sides >>>It does not like positions when the side to move threats check >>>or positions when there are pawns in the 1st or 8th rank. >>> >>>There is no problem with other positions including this position that is >>>illegal: >>> >>>[D]B1Bk4/1B6/B1B5/3B4/4B3/5B2/6B1/4K2B w - - 0 1 >>> >>>It is interesting to know how much time do your program need to see the draw(if >>>your program does not accept the position then you may remove one bishop from >>>the board). >> >>I think most (if not all) programs will have a very hard time solving this >>position. GreenLight did the same as Crafty in Pete's reply, but I was not at >>all surprised. >> >>>Can chest prove that there is no mate when the number of moves is not important? >> >>I don't think so, but I'm not sure. > >Normally not. Sometimes this (no mote) is obvious, and coded as "there is no >mate in 63". > > >>>I have no problem to prove it. >>>Uri >> >>I agree. Neither do I. So the questions are: >> >>1. What exactly do we do when we solve it? >>2. How can we get a computer to do the same? >> >>In answer to (1.), my proof was: >>In order to checkmate a king, you must be able to check him. Only the bishops >>can check the black king. The bishops are all on the white squares, so the king >>can always avoid check by not moving onto any white square, or be stalemated. > ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ >You have not yet proven this. The obvious part is: >If there is a dark square legally reachable, there is no mate in the next move. >Also: if there is no square at all reachable, there is no mate next, >since it is stalemate. > >But what, if the king is forced to enter a light square by zugzwang? >And such positions _can_ appear with this setup (in the corner). I agree that it was not a proof but it is easy to prove that white cannot mate. The distance in files or in ranks between the kings is at least 2(othewise if both are smaller than 2 the position is illegal) Let assume without loss of generality that the distance in files is at least 2(otherwise you can replace files by ranks for the rest of the proof). From the structure of the chess board the black king control a square at distance 1 from it in the same file. This square is not controled by the enemy king. It means that the black king cannot be in checkmate because the 2 squares in the same file(one of them is the square of the black king) have a different colour and the bishops can control at most 1 of them. Uri
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