Puzzles that highlight the finiteness of the chessboard 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.
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.