4

I'm curious as to whether there are compositions of chess puzzles/problems where the solution really emphasizes the boundedness of the board. Put differently, cases where the solution would be impossible on an infinitely large board.

  • 1
    There will be plenty of problems where the king gets mated on the border of the board. Do they qualify? – user1583209 Jan 18 '18 at 21:11
  • @user1583209 indeed they do, let's say for example the king+rook checkmate, but these are rather the more trivial examples. I was mainly hoping to find ones where some sort of a pattern/cycle breaks at some point because of the borders, I guess somewhat similar to phonon's king+bishop example. But in principle you are right that all border mates would be valid examples. I hope this clarifies it a bit :) – user929304 Jan 19 '18 at 16:04
  • None of the basic mates to a lonely king are possible on an infinite board – David May 28 '19 at 6:35
  • Which suggests a related problem - boards infinite in one direction (e.g. left-right) but finite in the orthogonal one. – Ian Bush May 29 '19 at 2:31
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Now that's a refreshingly different kind of question :)

It's probably easier to compose such a problem than to search for one, but that said, there's one that comes to mind:

 [Title "White to play and win"]
 [fen "8/5N1k/8/7b/1b5N/1K6/1B6/8 w - - 0 2"]

Hint:

You want to keep all 3 pieces as white in order to win. Try to set up a trap on the b4 bishop by setting up a discovery on the black king.

Solution:

1.Ng5+ Kh6 {only possible attempt to keep material} 2.Bc1 {Double threat: discovery on the king and threatening to take on b4, the trap is set} Ba5 {Any other move drops the bishop to a discovery check} 3.Ka4 Bb6 {only move again} 4.Kb5 Ba7 5.Ka6 Bb8 6.Kb7 {bishop falls.} From move 3.Ka4 it had become clear where this is going: the white king keeps shouldering the bishop until it hits a wall and cannot escape anymore. Now on an infinite board, this trap would have been impossible as the king and bishop dance would have continued endlessly.

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  • Too remarks: - I don't know why you wrote "zugzwang" after 2.Bc1. This is not zugzwang. - On an infinite chessboard, Black could even afford to give his Bb4, since 3 pieces vs 1 would be a draw (actually I'm not sure about 3 minor pieces vs a bare king on an infinite chessboard !) – Evargalo Jan 19 '18 at 8:32
  • @Evargalo Good remarks. This was hastily written, indeed one doesn't really call this a Zugzwang rather just a double threat. As for the infinite case, it doesn't even come to whether the 3 piece combo will be enough or not because black will be able to save the bishop anyway, and that already makes for a different scenario compared to the finite case altogether. This was just an example (among many one can come up with) to showcase the boundaries of the board being employed in a trap situation in order to illustrate the role of the finiteness. – Ellie Jan 19 '18 at 15:51
  • I agree (+1). My third remark: you should credit the author of this study (I am 99% sure he is André Chéron). – Evargalo Jan 19 '18 at 16:30
  • @Evargalo wow that'd be quite neat if you've correctly identified the author of the puzzle! I myself only recall having seen it as part of chess.com's tactics trainer. – Ellie Jan 19 '18 at 16:43
  • Refreshingly different? It's been years since the last time I've seen an actual chess question here! – David May 28 '19 at 6:37
2

Is this the sort of question you're looking for?

[Title "Erich Bartel. Augsburger Allgemeine, 10 Feb 2001, no.628. #6"]
[StartFlipped "0"]
[fen "8/7Q/3b2B1/1K6/3k4/4p3/8/8 w KQkq - 0 1"]

1.Bb1 Ke5 (e2? 2 Qe4+) 2. Qf5+ Kd4 3. Qe4+ Kc3 4. Qd3+ Kb2 5. Qc2+ Ka1 6. Qa2#

It is P1126265 in PDB (which, unfortunately, has a typo in White's mating move).

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0

I found this puzzle on Matplus the other day.

Here is the position.

[Title "H. Reddmann & T. Nalimov, #9, Original"]
[FEN "8/8/2B5/8/2N5/8/2K5/k2Bb3 w - - 0 1"]

It is white to play and checkmate black in 11 moves (the move number isn’t given in the link but it works.)

The Solution:

The idea here is to get one of the light squared bishops to hover beside the black king and be protected by the white king. Then the black king is trapped against the corner, ready to soon be killed by the white knight. If the board was infinite, there is no way that white could ever trap the white king with two bishops of the same color.

Here is one of the mating lines:

! 1. Be2 Bg3 2. Ba4 Bf2 3. Bb3 Be1 4. Ne5 Bd2 5. Nc6 Bc1 6. Bec4 Bb2 7. Ba2 Bd4 8. Bb1 Bc3 9. Bd3 Be1 10. Nd4 Bd2 11. Nb3#

And if the black king tries to move away:

! 1. Be2 Ka2 2. Ba4 Ka1 3. Bb3 Bf2 4. Na5 Be1 5. Nc6 Bd2 6. Bec4 Bc1 7. Ba2 Bb2 8. Bb1 Bc3 9. Bd5 Be1 10. Nd4 Bd2 11. Nb3#

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