Author: Sune Fischer
Date: 04:05:07 12/13/02
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On December 13, 2002 at 06:29:40, Uri Blass wrote: >>I think you are using some knowledge here, that white is not mated in steps >>1.-4. If I'm not mistaken you have to prove that 1.h4 f5 does not end the game. > >It seems obvious to be that after h4 when only the black pawns moves white is >not in check. > >After h4 I know that there may be black pawns only in 3 of the >squares(h7,h6,h5,g7,g6,g5,f7,f6,f5) > >I do not need to check every possibility to know that when the pawns are only in >these squares the white king is not in check. > >The proof is simple Yes, partly if you leave most of it to the rules of the game, then of course everything is proved fairly easy. >1.The only pieces that black has except king is pawns. >2.The only place for pawn to threat check is g7 >3.No black pawn can move to g7 > >conclusion: There is no way for black to threat check without promotion of the >pawns when the white king does not move. > >> >>Thus you have to examine that none of black's moves will mate white or stall >>mate black. This requires explicit search of each move and would give you a >>square root tree search. > >I proved that none of the black moves are going to mate white. I suppose this is given to you by the rules of the game. Lemma A 1) a black pawn that does not capture or is blocked or pinned is limited to moves down the file. 2) none of black's three pawns are blocked, pinned or can capture. 3) at every move of a black or a white pawn in direct line from the posted position, 2) will remain true until a pawn reaches a promoting square. 4) black are unable to give check with a pawn except on square b7, no black pawn can move to square b7 (rules of chess). Proof of 3) 1) Only sliding pieces can pinn pawns, there are no sliding pieces. 2) if white king does not move the black king cannot move, black can capture no pieces and no pawns will be blocked when kings do not move. Theorem A: White has a forced mate in 5 by the strategy of moving only his pawn and finally promote it to a rook or queen. Proof: By not moving the white king lemma A shows black can only move pawns down the file. By counting we argue that pawn will promote first and that the promoting position is a check mate of black. Ok, something along those lines should work. Most is given by reference to the rules of chess. The "problem" is in showing that no tree that folds out as the pawns start moving will change anything. -S.
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