user15078: 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.

user10380: 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#


user10380: 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.

user3594: 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. 
 
 


15078: <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>
 10380: <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>
 10380: <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>
 3594: <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 "White to play and win"]
 [fen "8/5N1k/8/7b/1b5N/1K6/1B6/8 w - - 0 2"]
</code></pre>

<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.stack.imgur.com/oTDC4.gif" alt=""></p>
</blockquote>
