Answers.Body: <p>Can Jacobi even solve such a puzzle?  I suppose one can have
  a program like Popeye solve 960 helpmates in 5, 4.5, 4, ...
  until it finds no solution to any of them,
  but that's not much fun to set up -- and it might not even work,
  because . . .</p>
  <pre><code>[Title &quot;Chess 960, after 0-0-0: Helpmate in 3.5, Black moving only pawns&quot;]
  [FEN &quot;bnrkqnrb/pppppppp/8/8/8/8/PPPPPPPP/BNKRQNRB w - - 0 0&quot;]
  
  1. pass a5 2. b3 a4 3. Bxg7 a3 4. Bb2 axb2#
  </code></pre>
  <p>White's first move was the Chess960 &quot;0-0-0&quot;,
  which I expect the Chess Stackexchange display won't do.
  Black then mates on move 4, moving only the a-pawn.</p>
  <p>This also means that 3.5 moves would suffice if each K weren't
  constrained to start between its R's, for example:</p>
  <pre><code>[Title &quot;Helpmate in 3.5, White moving only pawns&quot;]
  [FEN &quot;bqnrrknb/pppppppp/8/8/8/8/PPPPPPPP/BQNRRKNB w - - 0 0&quot;]
  
  1. h4 g6 2. h5 Bxb2 3. h6 Bg7 4. hxg7#
  </code></pre>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-08-30T12:11:32.957Z
Answers.Text: If the king was not constrained to start in between the 2 rooks, we can even do 2.5 moves : KRNQNBBR 1.a4 b5 2.Ka2 f5 3.Ka3 b4#
Answers.UserDisplayName: Evargalo
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-08-30T14:21:37.513Z
Answers.Text: That's 3.0 moves (and Black's 2nd is f5+), but you're right.
Answers.UserDisplayName: Noam D. Elkies
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-08-31T10:01:14.900Z
Answers.Text: Congratulations on 29, Noam! :)
Answers.UserDisplayName: Laska
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-08-29T02:14:15.503Z
Answers.LastActivityDate: 2024-08-29T02:14:15.503Z
Answers.UserDisplayName: Noam D. Elkies
Answers.Body: <p>I have a genuine h#3.5, which can be animated because there's no castling.</p>
  <pre><code>[Title &quot;Chess960: White moving only pawns helpmates in 3.5&quot;]
  [FEN &quot;rkrqnbbn/pppppppp/8/8/8/8/PPPPPPPP/RKRQNBBN w - - 0 0&quot;]
  
  1. a4 a5 2. b4 Ka7 3. f3+ Ka6 4. b5#
  </code></pre>
  <p>I have further checked with Jacobi that there are no shorter helpmates for any of the 960 game arrays. So h#3.5 is as good as one can get.</p>
  <p>Jacobi has checked exhaustively for all h#3.5 solutions. There is only one more matrix:</p>
  <pre><code>[Title &quot;Chess960: White moving only pawns helpmates in 3.5&quot;]
  [FEN &quot;rqkrbnnb/pppppppp/8/8/8/8/PPPPPPPP/RQKRBNNB w - - 0 0&quot;]
  
  1. d3 b6 2. b4 Kb7 3. g3+ Ka6 4. b5#
  </code></pre>
  <p>160/960 (i.e. one in six) of the starting positions allow h#3.5 with White only moving pawns. 108 give the first matrix, 42 give the second. Each valid starting position has exactly 8 solutions.</p>
  <p>The Jacobi instructions are:</p>
  <pre><code>stipulation h#3.5
  condition Chess960
  constraint Xa1-a1(0..0) Xb1-b1(0..0) Xc1-c1(0..0) Xd1-d1(0..0) Xe1-e1(0..0) Xf1-f1(0..0) Xg1-g1(0..0) Xh1-h1(0..0)
  </code></pre>
  <p>So White officers cannot move. The &quot;a1-a1&quot; substring etc excludes castling, which curiously in Jacobi is normally not prevented by &quot;(0..0)&quot;, the command to say that each piece must make at least 0 and at most 0 moves.</p>
  <p>It's easy to check that if White makes 5 pawn moves, with Black not moving, i.e. seriesmover, then we have 512 solutions, with 64 starting positions each having 8 solutions, e.g. (QBSSRKBR) 1.b3 2.f4 3.f5 4.f6 5.fxg7#</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-08-29T07:49:41.140Z
Answers.Text: You beat me by a half-move: bqrbnknr/pppppppp/8/8/8/8/PPPPPPPP/BQRBNKNR 1. g4 c5 2. Kg2 f5 3. Kh3 h5 4. Ng2 hxg4# Even if your move order is fixed, 3.f3/f4+ unfortunately ruins it as h#.
Answers.UserDisplayName: Hauke Reddmann
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-08-29T04:39:09.250Z
Answers.LastActivityDate: 2024-09-02T01:49:43.797Z
Answers.LastEditDate: 2024-09-02T01:49:43.797Z
Answers.UserDisplayName: Laska
Body: <p>Same as <a href="https://chess.stackexchange.com/questions/46091/checkmate-with-king-moves-only">this one</a> (also note <a href="https://chess.stackexchange.com/questions/19003/how-fast-can-checkmate-occur-by-just-moving-the-king">this</a>), only replace &quot;king&quot; by &quot;pawn&quot;. (I.e. shortest 960 helpmate, the mating side only uses pawn moves.) Yes, it can be done in the near-lying 5 moves with wK remaining put, even if that is a bit tricky. But...</p>
  <p>(Please use your brain first, <em>then</em> verify with Jacobi.)</p>
  
Tags: <checkmate><chess-variants><pawns><chess960><construction-task>
Title: Checkmate with pawn moves only
ThreadText: # Checkmate with pawn moves only
  
  (Asked by: username_0 on 2024-08-28)
  
  Same as [this one](https://chess.stackexchange.com/questions/46091/checkmate-with-king-moves-only) (also note [this](https://chess.stackexchange.com/questions/19003/how-fast-can-checkmate-occur-by-just-moving-the-king)), only replace "king" by "pawn". (I.e. shortest 960 helpmate, the mating side only uses pawn moves.) Yes, it can be done in the near-lying 5 moves with wK remaining put, even if that is a bit tricky. But...
  
  (Please use your brain first, *then* verify with Jacobi.)
  
  **Tags:** checkmate, chess-variants, pawns, chess960, construction-task
  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_3 on 2024-08-29. Score: 4 | Accepted answer
  
  I have a genuine h#3.5, which can be animated because there's no castling.
  [Title "Chess960: White moving only pawns helpmates in 3.5"]
  [FEN "rkrqnbbn/pppppppp/8/8/8/8/PPPPPPPP/RKRQNBBN w - - 0 0"]
  
  1. a4 a5 2. b4 Ka7 3. f3+ Ka6 4. b5#
  
  I have further checked with Jacobi that there are no shorter helpmates for any of the 960 game arrays. So h#3.5 is as good as one can get.
  Jacobi has checked exhaustively for all h#3.5 solutions. There is only one more matrix:
  [Title "Chess960: White moving only pawns helpmates in 3.5"]
  [FEN "rqkrbnnb/pppppppp/8/8/8/8/PPPPPPPP/RQKRBNNB w - - 0 0"]
  
  1. d3 b6 2. b4 Kb7 3. g3+ Ka6 4. b5#
  
  160/960 (i.e. one in six) of the starting positions allow h#3.5 with White only moving pawns. 108 give the first matrix, 42 give the second. Each valid starting position has exactly 8 solutions.
  The Jacobi instructions are:
  stipulation h#3.5
  condition Chess960
  constraint Xa1-a1(0..0) Xb1-b1(0..0) Xc1-c1(0..0) Xd1-d1(0..0) Xe1-e1(0..0) Xf1-f1(0..0) Xg1-g1(0..0) Xh1-h1(0..0)
  
  So White officers cannot move. The "a1-a1" substring etc excludes castling, which curiously in Jacobi is normally not prevented by "(0..0)", the command to say that each piece must make at least 0 and at most 0 moves.
  It's easy to check that if White makes 5 pawn moves, with Black not moving, i.e. seriesmover, then we have 512 solutions, with 64 starting positions each having 8 solutions, e.g. (QBSSRKBR) 1.b3 2.f4 3.f5 4.f6 5.fxg7#
  
  > **Comments:**
  > **username_0**: You beat me by a half-move: bqrbnknr/pppppppp/8/8/8/8/PPPPPPPP/BQRBNKNR 1. g4 c5 2. Kg2 f5 3. Kh3 h5 4. Ng2 hxg4# Even if your move order is fixed, 3.f3/f4+ unfortunately ruins it as h#.  
  
  ---
  
  ### Answer by username_1 on 2024-08-29. Score: 2
  
  Can Jacobi even solve such a puzzle?  I suppose one can have
  a program like Popeye solve 960 helpmates in 5, 4.5, 4, ...
  until it finds no solution to any of them,
  but that's not much fun to set up -- and it might not even work,
  because . . .
  [Title "Chess 960, after 0-0-0: Helpmate in 3.5, Black moving only pawns"]
  [FEN "bnrkqnrb/pppppppp/8/8/8/8/PPPPPPPP/BNKRQNRB w - - 0 0"]
  
  1. pass a5 2. b3 a4 3. Bxg7 a3 4. Bb2 axb2#
  
  White's first move was the Chess960 "0-0-0",
  which I expect the Chess Stackexchange display won't do.
  Black then mates on move 4, moving only the a-pawn.
  This also means that 3.5 moves would suffice if each K weren't
  constrained to start between its R's, for example:
  [Title "Helpmate in 3.5, White moving only pawns"]
  [FEN "bqnrrknb/pppppppp/8/8/8/8/PPPPPPPP/BQNRRKNB w - - 0 0"]
  
  1. h4 g6 2. h5 Bxb2 3. h6 Bg7 4. hxg7#
  
  > **Comments:**
  > **username_2**: If the king was not constrained to start in between the 2 rooks, we can even do 2.5 moves : KRNQNBBR 1.a4 b5 2.Ka2 f5 3.Ka3 b4#  
  > **username_1**: That's 3.0 moves (and Black's 2nd is f5+), but you're right.  
  > **username_3**: Congratulations on 29, Noam! :)  
  
  ---
  
  