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Chess Forum / Analysis / November 2007Castles, mate (Helpmate problem)
This occurred to me today on FICS, when someone needed an example of O-O mate. Premise: Starting from the initial position, construct the shortest possible game so that the final move is a mate delivered by castling. I could quickly come up with a solution in 9: 1 f4 f5 2 e4 fxe4 3 b3 Kf7 4 Bb2 Kg6 5 Bc4 Kf5 6 h4 Kxf4 7 h5 Kf5 8 h3 Nc6* 9 O-O# This is easily shortened to 8 by sacrificing the pawn at f5: 1 f4 f5 2 e4 fxe4 3 f5 Kf7 4 h4 Kf6 5 d4 Kxf5 6 Bc4 g6 7 Nh3 Nf6* 8 O-O# (* A number of other moves are possible also) and after a short little additional finagling I managed to remove a couple of wasted moves, producing a 7-move solution: 1 f4 f5 2 e4 fxe4 3 f5 Kf7 4 Nh3 Kf6 5 Bc4 Kxf5 6 d4 g6 7 O-O# Which looks pretty nice, really :) I'm not sure if a pure-mate version is possible (we have redundant coverage of g5 here); d4 is needed to cover e5 (which otherwise takes two moves to guard, as in the 9-mover), and the Knight can only go to h3 (f3 blocks the mate, and e2 results in an extra move being wasted to cover g4). It doesn't look that I can lower this below 7 moves, though someone else might be able to figure out a way to do so (castling itself involves 4 moves, plus it looks that White has to move the f-pawn once or twice in order to get it out of the way ...) Can it be done in 4 or 5 or 6? Sounds interesting, but I don't think a pure mate is possible since you have nightwatchmen sitting at the homebase; if pieces are unused, the mate is not pure, or? > Sounds interesting, but I don't think a pure mate is possible since > you have nightwatchmen sitting at the homebase; if pieces are > unused, the mate is not pure, or? `Pure' just means that each of the king's possible escape squares is covered by exactly one piece, doesn't it? It's not a problem if there are any number of pieces doing nothing, so long as they're not contributing to the checkmate, either. Dave.  SignatureDavid Richerby Incredible Flower (TM): it's like a www.chiark.greenend.org.uk/~davidr/ flower but it'll blow your mind! On Nov 9, 6:32 am, David Richerby <dav...@chiark.greenend.org.uk> wrote: > > Sounds interesting, but I don't think a pure mate is possible since > > you have nightwatchmen sitting at the homebase; if pieces are [quoted text clipped - 4 lines] > are any number of pieces doing nothing, so long as they're not > contributing to the checkmate, either. That is not true from a problemist's perspective, pure or ideal means each square is covered only once, and that there are no superfluous pieces at all. In a model mate, you can have idle king or pawns, nothing else. There is a magazine devoted to ideal or pure mate problems: Ideal Mate Review. I would think this would hold OTB as well since pure as a mating designation must be aesthetic in nature. One thing I was playing with was the shortest h# from the start with long castling. Its pretty neat, I find it hard not because of the longer time to long castling, but proper coverage of each piece; I always leave a square open. > This occurred to me today on FICS, when someone needed an example of O-O > mate. ... > Can it be done in 4 or 5 or 6? Well, there are examples of proof games - where the move order is uniquely determined and *Black* can mate in 6 from the initial position. See e.g. <URL:http://www.janko.at/Retros/Records/ShortestMate/ Geissler.htm> 1.e4 e5 2.Ke2 Ne7 3.Kf3 Nec6 4.Kg4 f5+ 5.Kxf5 Bc5 6.Qg4 0-0# Stephan SignatureStephan Bird MChem(Hons) AMRSC Currently in Caernarfon, Wales > Can it be done in 4 or 5 or 6? It can't be done in four. To play 4.O-O#, White must move his e-pawn or g-pawn, move his bishop, move his knight somewhere other than f3 and somehow lose his f-pawn. There's no time to move the f-pawn before it is captured and it must be captured by a black piece, not by a pawn because the capturing piece must move out of the way, because White doesn't have time to capture it. However, capturing the Pf2 with a black piece takes at least three moves. After these three moves, 4.O-O cannot give mate (if it's even legal) because the black king's still on e8. Similarly, to play 4... O-O#, Black must move his e/g pawn, move his bishop, move his knight somewhere other than f6 and lose his f-pawn without moving it. It takes White at least three moves to capture the Pf7 but, after those three moves, his king's still on e1, White has a piece of some kind on f7 and a pawn on f2 so 4... O-O cannot be check. I think similar reasoning should show that it can't be done in five, either, but it's more complicated because there's a bit more freedom in the moves. A useful trick is likely to be that, if the losing side captures the winner's unmoved f-pawn on move three, on move four, he must move the capturing piece out of the way but, on move five, he can move it back to f2/f7 so any check cannot be mate. But we also need to consider cases where the loser captures the f-pawn after it has been moved or places a piece on his opponent's K3 or KN3, which the winner captures with his f-pawn to open the file. I'll let somebody else think about that. Dave. SignatureDavid Richerby Hilarious Sushi (TM): it's like a raw www.chiark.greenend.org.uk/~davidr/ fish but it's a bundle of laughs! |
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