Answers.Body: <p>Full solution attempt:</p>
  <p>Last move obviously was <code>exZf1=Q+</code>, with yet unspecified piece <code>Z</code>. If that was original <code>Bf1</code>, <code>a2</code> is promoted. Impossible, as <code>a2</code> can only promote on <code>b8</code> given that it can only promote by <code>a6xQb7-b8</code> (the black f pawn promoted on f1, as already established, leaving only the black queen as victim for the white a pawn) - wrong color. Thus <code>Ba2</code> is original and <code>a2</code> promoted, again by <code>a6xQb7-b8</code>. We thus already know the promoted figure Z is either <code>Q</code> or <code>N</code> (<code>R</code> can't get out again).  Here is a <code>N</code> attempt, I have a good hunch that <code>Q</code> is faster (<code>Q-b7-a6-f1</code>) and even the moves are unique.</p>
  <pre><code>[FEN &quot;rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1&quot;]
  
  1. a4 b6 2. a5 Bb7 3. a6 Bc6 4. e4 Qc8 5. Bc4 Qb7 6. axb7 Na6 7. b8=N Bb7 8. Nc6 f5 9. d3 f4 10. Be3 fxe3 11. f3 e2 12. Nd4 Nb8 13. Nf5 Bc8 14. Ng3 Bb7 15. Ba2 Bc8 16. Nf1 exf1=Q+
  </code></pre>
  <p>A simple counting of White moves proves that a <code>N</code> solution can't be improved. <code>Q</code> could attain 14 moves, here Black also needs 14 moves minimally - so this could work out if timed carefully. But I don't see a trick to actually save the one black move: with a square z5, I could play Bz5 and avoid wasting the white/black tempo, so I am at 15.</p>
  <pre><code>[FEN &quot;rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1&quot;]
  
  1. a4 b6 2. a5 Ba6 3. e4 Bb5 4. Bc4 Qc8 5. a6 Qb7 6. axb7 Nc6 7. Bb3 Ba6 8.
  b8=Q+ Bc8 9. Qb7 f6 10. Qa6 f5 11. Qf1 f4 12. d3 Nb8 13. Be3 fxe3 14. Ba2 e2
  15. f3 exf1=Q+
  </code></pre>
  <p>Optimality proof attempt: White obviously does need 14 moves (one tempo was wasted on Bb3). But then let's retro-move further from the final diagram: White can only take back &quot;neutrally&quot; <code>f3</code>. But another move pair is needed before <code>Be3</code>, which forces <code>d3</code> before that, and the white queen can't get to f1 anymore! White has no such move, obviously, so a tempo like <code>Bb3</code> must be inserted.</p>
  <p>5 minutes for the logic :-)</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-03-29T07:50:25.800Z
Answers.Text: @CarloWood: In the chess problem genre your puzzle fits in, it is usually preferred when the solution is absolutely unique. Here, for example, you could have replaced f3 by h3+Rh2 (and some black move, it's a random example) so that White gets just right in time. The Bc8 could capture a White piece just for fun to make its way unique too. Of course the fact that it returns to c8 is a great plus. I'll show the problem to the experts, maybe they find a way.
Answers.UserDisplayName: Hauke Reddmann
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-03-26T14:54:38.357Z
Answers.LastActivityDate: 2022-03-28T11:28:22.210Z
Answers.LastEditDate: 2022-03-28T11:28:22.210Z
Answers.UserDisplayName: Hauke Reddmann
Answers.Body: <p>The last piece captured was a white <strong>knight</strong> on f1.</p>
  <ul>
  <li>The last move must have been exf1=Q.</li>
  <li>With a bishop on a2, the captured piece on f1 must have been promoted before.</li>
  <li>It is white's a-pawn then that must have reached b8 via a6-axb7-b8.</li>
  <li>Promotion to rook or bishop can be excluded since they cannot return to f1 in above pawn structure.</li>
  <li>Promotion to queen can be excluded wrt the condition of minimal game length.</li>
  </ul>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-03-26T15:05:21.217Z
Answers.LastActivityDate: 2022-03-26T15:05:21.217Z
Answers.UserDisplayName: starrin
Body: <p>This is a puzzle that I made a while ago, but never really published anywhere before (although I posted it on an obscure Dutch telegram channel).</p>
  <p>The question is simple: what was the piece that was captured last?
  Hence, the answer can be: rook, knight, bishop or queen.</p>
  <p>However, you can't know - because there are multiple ways to reach
  this position - so there is extra information: this position was reached
  in the minimum number of moves possible.</p>
  <p>As answer - just post a game-diagram (PGN) that shows a way to reach the
  given position in the fastest way possible.</p>
  <pre><code>[FEN &quot;rnb1kbnr/p1ppp1pp/1p6/8/4P3/3P1P2/BPP3PP/RN1QKqNR w KQkq - 0 1&quot;]
  </code></pre>
  <p>Have fun!</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2022-03-26T14:31:19.423Z
Comments.Text: If you have fun with these kinds of chess puzzles, I warmly recommend http://matplus.net, a forum for chess problem composers. At last they rather need only several minutes for solving :-)
Comments.UserDisplayName: Hauke Reddmann
Tags: <problems><retrograde-analysis>
Title: Which piece was captured last - knowing that this position was reached in the minimum number of moves possible?
ThreadText: # Which piece was captured last - knowing that this position was reached in the minimum number of moves possible?
  
  (Asked by: username_0 on 2022-03-26)
  
  This is a puzzle that I made a while ago, but never really published anywhere before (although I posted it on an obscure Dutch telegram channel).
  
  The question is simple: what was the piece that was captured last?
  Hence, the answer can be: rook, knight, bishop or queen.
  
  However, you can't know - because there are multiple ways to reach
  this position - so there is extra information: this position was reached
  in the minimum number of moves possible.
  
  As answer - just post a game-diagram (PGN) that shows a way to reach the
  given position in the fastest way possible.
  
  ```
  [FEN "rnb1kbnr/p1ppp1pp/1p6/8/4P3/3P1P2/BPP3PP/RN1QKqNR w KQkq - 0 1"]
  
  ```
  
  Have fun!
  
  **Tags:** problems, retrograde-analysis
  
  > **Comments:**
  > **username_1**: If you have fun with these kinds of chess puzzles, I warmly recommend http://matplus.net, a forum for chess problem composers. At last they rather need only several minutes for solving :-)  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_1 on 2022-03-26. Score: 5 | Accepted answer
  
  Full solution attempt:
  
  Last move obviously was `exZf1=Q+`, with yet unspecified piece `Z`. If that was original `Bf1`, `a2` is promoted. Impossible, as `a2` can only promote on `b8` given that it can only promote by `a6xQb7-b8` (the black f pawn promoted on f1, as already established, leaving only the black queen as victim for the white a pawn) - wrong color. Thus `Ba2` is original and `a2` promoted, again by `a6xQb7-b8`. We thus already know the promoted figure Z is either `Q` or `N` (`R` can't get out again). Here is a `N` attempt, I have a good hunch that `Q` is faster (`Q-b7-a6-f1`) and even the moves are unique.
  
  ```
  [FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]
  
  1. a4 b6 2. a5 Bb7 3. a6 Bc6 4. e4 Qc8 5. Bc4 Qb7 6. axb7 Na6 7. b8=N Bb7 8. Nc6 f5 9. d3 f4 10. Be3 fxe3 11. f3 e2 12. Nd4 Nb8 13. Nf5 Bc8 14. Ng3 Bb7 15. Ba2 Bc8 16. Nf1 exf1=Q+
  
  ```
  
  A simple counting of White moves proves that a `N` solution can't be improved. `Q` could attain 14 moves, here Black also needs 14 moves minimally - so this could work out if timed carefully. But I don't see a trick to actually save the one black move: with a square z5, I could play Bz5 and avoid wasting the white/black tempo, so I am at 15.
  
  ```
  [FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]
  
  1. a4 b6 2. a5 Ba6 3. e4 Bb5 4. Bc4 Qc8 5. a6 Qb7 6. axb7 Nc6 7. Bb3 Ba6 8.
  b8=Q+ Bc8 9. Qb7 f6 10. Qa6 f5 11. Qf1 f4 12. d3 Nb8 13. Be3 fxe3 14. Ba2 e2
  15. f3 exf1=Q+
  
  ```
  
  Optimality proof attempt: White obviously does need 14 moves (one tempo was wasted on Bb3). But then let's retro-move further from the final diagram: White can only take back "neutrally" `f3`. But another move pair is needed before `Be3`, which forces `d3` before that, and the white queen can't get to f1 anymore! White has no such move, obviously, so a tempo like `Bb3` must be inserted.
  
  5 minutes for the logic :-)
  
  > **Comments:**
  > **username_1**: @username_0: In the chess problem genre your puzzle fits in, it is usually preferred when the solution is absolutely unique. Here, for example, you could have replaced f3 by h3+Rh2 (and some black move, it's a random example) so that White gets just right in time. The Bc8 could capture a White piece just for fun to make its way unique too. Of course the fact that it returns to c8 is a great plus. I'll show the problem to the experts, maybe they find a way.  
  
  ---
  
  ### Answer by username_2 on 2022-03-26. Score: 0
  
  The last piece captured was a white **knight** on f1.
  
  * The last move must have been exf1=Q.
  * With a bishop on a2, the captured piece on f1 must have been promoted before.
  * It is white's a-pawn then that must have reached b8 via a6-axb7-b8.
  * Promotion to rook or bishop can be excluded since they cannot return to f1 in above pawn structure.
  * Promotion to queen can be excluded wrt the condition of minimal game length.
  
  
  ---
  
  