Answers.Body: <p>Now that's a refreshingly different kind of question :)</p>
  <p>It's probably easier to compose such a problem than to search for one, but that said, there's one that comes to mind:</p>
  <pre><code> [Title &quot;White to play and win&quot;]
   [fen &quot;8/5N1k/8/7b/1b5N/1K6/1B6/8 w - - 0 2&quot;]
  </code></pre>
  <p>(Study by <a href="https://en.wikipedia.org/wiki/Henri_Rinck" rel="nofollow noreferrer">Henri Rinck</a>)</p>
  <p><strong>Hint:</strong></p>
  <blockquote class="spoiler">
  <p> You want to keep all 3 pieces as white in order to win. Try to set up a trap on the <code>b4</code> bishop by setting up a discovery on the black king.</p>
  </blockquote>
  <p><strong>Solution:</strong></p>
  <blockquote class="spoiler">
  <p> 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 <code>3.Ka4</code> 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.
  
   <img src="https://i.sstatic.net/oTDC4.gif" alt="" /></p>
  </blockquote>
  
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Answers.Text: 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 !)
Answers.UserDisplayName: Evargalo
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Answers.Text: @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.
Answers.UserDisplayName: Ellie
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Answers.Text: I agree (+1). My third remark: you should credit the author of this study (I am 99% sure he is André Chéron).
Answers.UserDisplayName: Evargalo
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Answers.Text: @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.
Answers.UserDisplayName: Ellie
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Answers.Text: Refreshingly different? It's been years since the last time I've seen an actual chess question here!
Answers.UserDisplayName: David
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Answers.Text: @David Note that this post and answer are more than a year old :-) What kind of chess questions you mean? (that you haven't seen) Would these [1](https://chess.stackexchange.com/a/23893/15078), [2](https://chess.stackexchange.com/a/23687/15078), [3](https://chess.stackexchange.com/a/19898/15078), ... among others not qualify as proper interesting chess questions? :p
Answers.UserDisplayName: user929304
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Answers.Text: On an infinite chess board, the king wouldn't be able to chase the bishop to begin with; Black could simply do 2 ... h10.
Answers.UserDisplayName: Acccumulation
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Answers.UserDisplayName: Ellie
Answers.Body: <p>Is this the sort of problem you're looking for?</p>
  <pre><code>[Title &quot;Erich Bartel. Augsburger Allgemeine, 10 Feb 2001, no.628. #6&quot;]
  [StartFlipped &quot;0&quot;]
  [fen &quot;8/7Q/3b2B1/1K6/3k4/4p3/8/8 w KQkq - 0 1&quot;]
  
  1. Bb1! Ke5 (1... e2? 2. Qe4+) 2. Qf5+ Kd4 3. Qe4+ Kc3 4. Qd3+ Kb2 5. Qc2+ Ka1 6. Qa2#
  </code></pre>
  <p>It is <a href="https://pdb.dieschwalbe.de/P1126265" rel="nofollow noreferrer">P1126265</a> in the PDB.</p>
  
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Answers.LastEditDate: 2021-05-01T19:20:02.390Z
Answers.UserDisplayName: Rosie F
Answers.Body: <p>A problem must surely demonstrate the finiteness of the board if it has two twins, the solutions are essentially different, and the twinning is by shifting every unit 1 file to the right. Or, regarding the units as fixed, by cutting the empty h-file off the right-hand side and pasting it to the left-hand side.</p>
  <pre><code>[Title &quot;Heinz Däubler. Augsburger Allgemeine, 23 Sep 2006, no. 919a. P1197652&quot;]
  [fen &quot;1B6/1B6/8/1k6/8/1K6/8/1N6 w - - 0 1&quot;]
  [StartFlipped &quot;0&quot;]
  
  1. Ba7 Ka5 2. Kc4 {Na3? stalemates} Ka4 3. Bb8 Ka5 4. Bc7+ Ka4 5. Bc6#
  </code></pre>
  <p>and</p>
  <pre><code>[Title &quot;ditto, all 1 file to the right&quot;]
  [fen &quot;2B5/2B5/8/2k5/8/2K5/8/2N5 w - - 0 1&quot;]
  [StartFlipped &quot;0&quot;]
  
  1. Bb7 Kb5 2. Nb3 {Kd4? Kb4 3 and bK escapes to the a-file and White can't mate in time} Ka4 3. Bd6 Kb5 4. Bc5 Ka4 5. Bc6#
  </code></pre>
  
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Answers.UserDisplayName: Rosie F
Body: <p>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.</p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-01-18T21:11:05.160Z
Comments.Text: There will be plenty of problems where the king gets mated on the border of the board. Do they qualify?
Comments.UserDisplayName: user1583209
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-01-19T16:04:29.990Z
Comments.Text: @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 :)
Comments.UserDisplayName: user929304
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-05-28T06:35:45.083Z
Comments.Text: None of the basic mates to a lonely king are possible on an infinite board
Comments.UserDisplayName: David
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2019-05-29T02:31:31.237Z
Comments.Text: Which suggests a related problem - boards infinite in one direction (e.g. left-right) but finite in the orthogonal one.
Comments.UserDisplayName: Ian Bush
Tags: <problems><mathematics>
Title: Puzzles that highlight the finiteness of the chessboard
ThreadText: # Puzzles that highlight the finiteness of the chessboard
  
  (Asked by: username_0 on 2018-01-18)
  
  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.
  
  **Tags:** problems, mathematics
  
  > **Comments:**
  > **username_1**: There will be plenty of problems where the king gets mated on the border of the board. Do they qualify?  
  > **username_0**: @username_1 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 :)  
  > **username_2**: None of the basic mates to a lonely king are possible on an infinite board  
  > **username_3**: Which suggests a related problem - boards infinite in one direction (e.g. left-right) but finite in the orthogonal one.  
  
  ---
  
  ## 3 answers
  
  ### Answer by username_4 on 2018-01-18. Score: 6
  
  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"]
  
  (Study by Henri Rinck)
  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.
  
  > **Comments:**
  > **username_5**: 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 !)  
  > **username_4**: @username_5 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.  
  > **username_5**: I agree (+1). My third remark: you should credit the author of this study (I am 99% sure he is André Chéron).  
  > **username_4**: @username_5 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.  
  > **username_2**: Refreshingly different? It's been years since the last time I've seen an actual chess question here!  
  > **username_0**: @username_2 Note that this post and answer are more than a year old :-) What kind of chess questions you mean? (that you haven't seen) Would these [1](https://chess.stackexchange.com/a/23893/15078), [2](https://chess.stackexchange.com/a/23687/15078), [3](https://chess.stackexchange.com/a/19898/15078), ... among others not qualify as proper interesting chess questions? :p  
  > **username_6**: On an infinite chess board, the king wouldn't be able to chase the bishop to begin with; Black could simply do 2 ... h10.  
  
  ---
  
  ### Answer by username_7 on 2019-05-28. Score: 3
  
  Is this the sort of problem 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 (1... e2? 2. Qe4+) 2. Qf5+ Kd4 3. Qe4+ Kc3 4. Qd3+ Kb2 5. Qc2+ Ka1 6. Qa2#
  
  It is P1126265 in the PDB.
  
  
  ---
  
  ### Answer by username_7 on 2021-07-26. Score: 1
  
  A problem must surely demonstrate the finiteness of the board if it has two twins, the solutions are essentially different, and the twinning is by shifting every unit 1 file to the right. Or, regarding the units as fixed, by cutting the empty h-file off the right-hand side and pasting it to the left-hand side.
  [Title "Heinz Däubler. Augsburger Allgemeine, 23 Sep 2006, no. 919a. P1197652"]
  [fen "1B6/1B6/8/1k6/8/1K6/8/1N6 w - - 0 1"]
  [StartFlipped "0"]
  
  1. Ba7 Ka5 2. Kc4 {Na3? stalemates} Ka4 3. Bb8 Ka5 4. Bc7+ Ka4 5. Bc6#
  
  and
  [Title "ditto, all 1 file to the right"]
  [fen "2B5/2B5/8/2k5/8/2K5/8/2N5 w - - 0 1"]
  [StartFlipped "0"]
  
  1. Bb7 Kb5 2. Nb3 {Kd4? Kb4 3 and bK escapes to the a-file and White can't mate in time} Ka4 3. Bd6 Kb5 4. Bc5 Ka4 5. Bc6#
  
  
  ---
  
  