user30167: I've had this puzzle rattling around in my brain for the past few days and I want to know what you all make of it.
Imagine chess played on a board with eight ranks and an infinite number of files. Black has a single rook on a1. White has an infinite number of pawns, one on every square in the first rank besides a1.
The rules here are slightly different from normal chess.


White's goal is to capture the rook. Black's goal is to never get captured.
White's pawns can only move one space forward and never have the option to move forward two spaces. They still capture diagonally.
White may move one pawn off of the first rank, and any number of pawns already off the first rank simultaneously (notated with an ampersand).


Is White guaranteed to capture Black's rook at some point in time, or does Black have a strategy to survive? I think White has a guaranteed victory, but I can't say for sure. Consider the following string of moves.
1.b2 Rxc1
2.b3&d2 Rxe1
3.b4&d3&f2 Rxg1
4.b5&d4&f3&h2 Rxi1
5.b6&d5&f4&h3&j2 Rb1
6.b7&d6&f5&h4&j3&k2 Rxb7
7.d7&f6&h5&j4&k3&l2 Rxd7
8.f7&h6&j5&k4&l3&m2 Rxf7
9.h7&j6&k5&l4&m3&n2 Rxh7
10.j7&k6&l5&m4&n3&o2

Now Black is stuck. If they play 10... Rxj7, then White follows with 11. kxj7 and wins. If they do anything else, then 11. j8=Q is sure to follow, which spells out doom for Black. Does Black have a more optimal strategy that leads to their survival, or is this it?

user4418: It is trivially a win for white even on an 8x8 board
[fen "8/8/8/8/8/8/8/rPPPPPPP w - - 0 1"] 

1. h2 Rxb1 2. g2 null 3. h3 Rxc1 4. f2 null 5. g3 null 6. h4 Rxd1 7. e2 null 8. f3 null 9. g4 null 10. h5 Re1 11. e3 null 12. f4 null 13. g5 null 14. h6 Rxe3 15. f5 null 16. g6 null 17. h7 Rf3 18. f6 null 19. g7 null 20. h8=Q Rxf6


30167: <p>I've had this puzzle rattling around in my brain for the past few days and I want to know what you all make of it.</p>
<p>Imagine chess played on a board with eight ranks and an infinite number of files. Black has a single rook on a1. White has an infinite number of pawns, one on every square in the first rank besides a1.</p>
<p>The rules here are slightly different from normal chess.</p>
<blockquote>
<ol>
<li>White's goal is to capture the rook. Black's goal is to never get captured.</li>
<li>White's pawns can only move one space forward and never have the option to move forward two spaces. They still capture diagonally.</li>
<li>White may move one pawn off of the first rank, and any number of pawns already off the first rank simultaneously (notated with an ampersand).</li>
</ol>
</blockquote>
<p>Is White guaranteed to capture Black's rook at some point in time, or does Black have a strategy to survive? I <em>think</em> White has a guaranteed victory, but I can't say for sure. Consider the following string of moves.</p>
<pre><code>1.b2 Rxc1
2.b3&amp;d2 Rxe1
3.b4&amp;d3&amp;f2 Rxg1
4.b5&amp;d4&amp;f3&amp;h2 Rxi1
5.b6&amp;d5&amp;f4&amp;h3&amp;j2 Rb1
6.b7&amp;d6&amp;f5&amp;h4&amp;j3&amp;k2 Rxb7
7.d7&amp;f6&amp;h5&amp;j4&amp;k3&amp;l2 Rxd7
8.f7&amp;h6&amp;j5&amp;k4&amp;l3&amp;m2 Rxf7
9.h7&amp;j6&amp;k5&amp;l4&amp;m3&amp;n2 Rxh7
10.j7&amp;k6&amp;l5&amp;m4&amp;n3&amp;o2
</code></pre>
<p>Now Black is stuck. If they play 10... Rxj7, then White follows with 11. kxj7 and wins. If they do anything else, then 11. j8=Q is sure to follow, which spells out doom for Black. Does Black have a more optimal strategy that leads to their survival, or is this it?</p>
 4418: <p>It is trivially a win for white even on an 8x8 board</p>
<pre><code>[fen &quot;8/8/8/8/8/8/8/rPPPPPPP w - - 0 1&quot;] 

1. h2 Rxb1 2. g2 null 3. h3 Rxc1 4. f2 null 5. g3 null 6. h4 Rxd1 7. e2 null 8. f3 null 9. g4 null 10. h5 Re1 11. e3 null 12. f4 null 13. g5 null 14. h6 Rxe3 15. f5 null 16. g6 null 17. h7 Rf3 18. f6 null 19. g7 null 20. h8=Q Rxf6
</code></pre>
