Answers.Body: <p>It’s not really a matter of “correctness”. This is clearly not an orthodox problem. The issue is more whether the stipulation is “fair” and “elegant”.</p>
  <p>And I think it probably is fair. The problems are simple enough that the trick with the stipulation is guessable. I much prefer the second &quot;heavier&quot; version over the &quot;lighter&quot; one, although I haven't rechecked the retro play. I trust that the logic which worked in the earlier version works again.</p>
  <p>A alternative is to add the word &quot;Who?&quot; to the stipulation, indicating that the solver has to figure out who is the mater. But this makes the problem less elegant.</p>
  <p>Given that Black can unilaterally seize the move by immediately castling, White cannot prevent it. So the question becomes: what can #3 mean? Lateral thinking gives the answer.</p>
  <p>The basis principle of AP is clear: that executing castling can &quot;prove&quot; that other entangled rights are enabled. However the idea has not been formalized. Areas of complication include: (1) extension of the idea from RS (where it originated) to PRA (2) handling of information from multiple twins (3) AP Prioritat, and what suffices as a refutation (4) interaction with other conceits (such as here the reversal of player delivering the mate). There is no single agreed perspective on all of these, even amongst the experts. In the absence of unanimity, we should welcome the diversity, and acknowledge that your problem finds a unique place in this merry throng.</p>
  <p>The forward play is much better than your earlier dualed version. The checking keys are still defects, but may be difficult to avoid. I think the problem is still of publishable quality (except that it has been self-published here in chess.se). If you could find a matrix for your idea that avoids the checking keys that would be even more impressive.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-06-21T11:05:20.530Z
Answers.Text: In my opinion, here (1. exd7+ Kf8) move 1. ... Kf8 is not defensive, because white is directly threatening 2. d7xc8=Q# and only Bxd7 and Kd8 are defensive moves. And the Kf8 move is kind of half cooperative.
Answers.UserDisplayName: Элси Ринген
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-06-21T11:25:54.020Z
Answers.Text: @ЭлсиРинген the notions of threat & defence only apply with a non-checking key! So Popeye treats all the Black moves Bxd7, Kd8 & Kf8 as equally valid options, the last being dualed.
Answers.UserDisplayName: Laska
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Answers.CreationDate: 2024-06-21T11:40:23.623Z
Answers.Text: Checkmate in 2 moves (Who?) AP. 
  In my opinion (Who?) This is a bad idea.
  This will change the initial condition "by default, the move in white's position" to "whose move in the position is unknown". 
  This will create such confusion: white can, if black does not apply AP; black can, by applying AP; black can, without using AP (there is also a dual).
  Removing AP from the task is also not good: two answers and one with a dual.
Answers.UserDisplayName: Элси Ринген
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-06-21T12:15:29.583Z
Answers.Text: "This is the silly idea of A Posteriori Type Keym."
  
  Perhaps it is better to make sure that white does not have a checkmate at all in two moves and the ability to checkmate black is the only way to complete the task?
Answers.UserDisplayName: Элси Ринген
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-06-21T14:19:27.127Z
Answers.Text: There is a difference between who moves first and who delivers the mate. halfduplex flips both of them. Who? flips the mate delivery. But this is not quite certain I agree. I think that with the AP folk will get to the right answer, but without it’s not clear. I don’t like stipulations which require narrow semantics interpretations but sometimes it’s difficult to avoid them without being clunky. Up to you
Answers.UserDisplayName: Laska
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Answers.CreationDate: 2024-06-21T15:52:35.923Z
Answers.Text: I didn't argue with Popeye. I redid the Checkmate task in three moves. I don't like duals.
Answers.UserDisplayName: Элси Ринген
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-06-21T16:50:18.187Z
Answers.Text: To be honest, the idea of a pawn check on the first move seemed dubious to me from the very beginning.
Answers.UserDisplayName: Элси Ринген
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-06-22T15:34:06.203Z
Answers.Text: Rarely have I had to write an answer so many times in response to a changing question, for one measly upvote! :-)
Answers.UserDisplayName: Laska
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Answers.CreationDate: 2024-06-22T16:37:55.057Z
Answers.Text: About the last paragraph of the answer. In my opinion, neither white nor black can avoid the check on the first move here. Otherwise, the other side will immediately torture you with their checks.
Answers.UserDisplayName: Элси Ринген
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Answers.CreationDate: 2024-06-22T17:18:20.187Z
Answers.Text: I didn't quite understand the passage about AP not being formalized. As far as I know, AP has a clear formulation: "If the right to castling is required to solve a problem, then castling must be performed during the solution process, regardless of whether it is necessary for the solution or not."
  And all the tasks I know fall under this formulation.
Answers.UserDisplayName: Элси Ринген
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Answers.CreationDate: 2024-06-23T11:26:30.380Z
Answers.Text: I've edited my answer to address the last two comments by Elsie
Answers.UserDisplayName: Laska
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Answers.UserDisplayName: Laska
Answers.Body: <p>Colleague Laska suggested considering the issue in the plane of correctness and elegance. I agree with this statement of the question. And I will try to describe my vision.</p>
  <p><strong>1. Correctness</strong></p>
  <p>Tasks in which the parties have any special rights in the initial position (en-passant, castling), as a rule, may have different versions of the game in the past. There are usually two of them, but there may be more (as far as I know, five at most).</p>
  <p>And there are two methods for solving such problems:</p>
  <p>A) divide the problem into two parts with a different game in the past and solve both parts separately (together you will get one complete solution);</p>
  <p>B) choose one of the two options in the past by making an evidentiary move (this is always castling).</p>
  <p>Option B) is simple, has a clear name RS (Retro Strategy), everything is simple with it.</p>
  <p>Option A) is more complicated. There is a constant confusion with PRA (partial retroanalysis). The PRA uses the same method (dividing the task into parts based on different rights in the initial position), but the PRA Convention has a bunch of restrictions (there must be at least two special rights, they must be dependent on each other, etc.). Therefore, for cases of different games in the past, but not falling under the PRA Convention, it is better to use another name. I suggest RV (retro versions), but you can do any other. It's not about the name.</p>
  <p>If we consider the tasks of AP (A Posteriori) by type, then there are two past ones in Petrovic type:</p>
  <p>a) white has the right to en-passant and has the right to castling;</p>
  <p>b) whites have neither one nor the other right.</p>
  <p>There are also two previous ones in AP (Keym type, white):</p>
  <p>a) white has the right to move in position, but there is no castling;</p>
  <p>b) black is in position and white has the right to castling.</p>
  <p>In both cases, white cannot complete the task in both versions of the past and cannot complete it in the default version of the past, but can complete the task in another version of the past. And they only need to prove it by making a castling. The only difference between AP and simple RS is that we choose an option, not just by making a castling (the choice of the past here happens automatically), but first we choose the past, and then, as proof of the choice, we castling later.</p>
  <p>It is important here that in both cases white has the right to choose: they can leave the option that goes by default; they can choose another one. Black cannot influence white's choice in any way.</p>
  <p>The AP case is more interesting (Keym type, black).</p>
  <p>There are also two previous ones here:</p>
  <p>a) a move in white's position, black does not have the right to castling;</p>
  <p>b) a move in black's position, black has the right to castling.</p>
  <p>But it is important that black now has the choice of an option from the past and they can choose any one. Therefore, white needs to beat black in both ways to solve the problem.
  If in at least one variant white cannot complete the task, in the usual case it is the unsolvability of the task, marriage.
  And the solution to the problem here can only be saved if black completes the task instead of white. Then the problem will have a solution and it will be the only one, because it was performed by a party who had the opportunity to choose options from the past.</p>
  <p>By itself, completing a task with blacks instead of whites is not a new thing. In half of the &quot;Checkmate in 1 move&quot; tasks, black is checkmated.
  Is there a difference between the tasks &quot;Checkmate in 1 move&quot; and &quot;Checkmate in 4 moves&quot;? In my opinion, no. All these are tasks of the same type &quot;Checkmate in N moves&quot;.</p>
  <p>Only the justification for completing the task for black is slightly different. This is usually just a retroanalysis of the position, where it turns out that the position during white's move is illegal. Here, black proves the illegality of the position during the course of white, using the opportunities provided by the AP agreement.</p>
  <p>That's how it is...</p>
  <p><strong>2. Elegance</strong></p>
  <p>The task was conceived simply as a joke. However, according to the rules (and not as it sometimes happens, where the rules must first be thought out ... :)). It was done in a hurry. Just to test the idea. Apply the same technique in the type of Case for blacks that is usually used by whites.</p>
  <p>And I completely agree with Lask's colleague that shahi on the first move is &quot;not good at all.&quot;  And for a long time it seemed to me that it was impossible to get rid of them with such a statement of the question. But it turned out that it was possible. At least on the first move (and white will have no time for checks at all).</p>
  <pre><code>4k2r/Np4p1/RR1pPB2/4p3/N1P5/p1p1P1P1/rP2P1PP/5KQ1 w - - 1 13
  </code></pre>
  <p><strong>Checkmate in 4 moves</strong></p>
  <p>White does not have the opportunity to check on the first move at all. And considering that black has the opportunity to put two checks at any pause, white needs a checkmate in two moves. And he is!</p>
  <p><strong>1. Nc6 Ra1+ 2. Kf2 Rf1+ 3. Kxf1(Qxf1)
  3. ... bxa6 4. Rb8#;</strong> 3. ... gxf6 4. Ra8#</p>
  <p>But this is a fiction and a mirage, because by a strong-willed decision, black takes the move for himself.</p>
  <p><strong>1. 0-0</strong> (I suffered for a very long time so that, in addition to 1. 0-0, I could just pass 1. Rf8. Otherwise, it would just be a simple duplex).</p>
  <p>Black threatens with a simple mat in two moves.</p>
  <ol>
  <li><p>... Kf2 (e4, e7) 2. Rxf6 ... 3. Ra1#</p>
  </li>
  <li><p>... Ke1 2. Ra1 ... 3. Rxf6#</p>
  </li>
  </ol>
  <p>The most white can do is delay the inevitable by one move.</p>
  <p><strong>1. 0-0</strong></p>
  <p><strong>1. ... Qf2 2. Ra1+ Qe1 3. Rxf6+ Kg1 4. Rxe1#</strong></p>
  <p><strong>1. ... Nxc3 2. Ra1+ Nb1(d1) 3. Rxb1(d1)+ Kf2 4. Rxf6#</strong></p>
  <p><strong>1. ... bxc3 3. Ra1+ Rb1 3. Rxb1+ Kf2 4. Rxf6#</strong></p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2024-06-24T21:31:32.130Z
Answers.LastActivityDate: 2024-06-24T22:12:05.957Z
Answers.LastEditDate: 2024-06-24T22:12:05.957Z
Answers.UserDisplayName: Элси Ринген
Body: <p>Again, I composed the task, but doubts crept in. Is everything really as I think it is?</p>
  <pre><code>4k2r/4p3/4P3/7N/8/P7/rP1PP1P1/5KQR w - - 1 13
  </code></pre>
  <pre><code>2b1k2r/1p1pp1p1/4P3/p6N/6P1/2P5/1PrPP1P1/1B3KQR w - - 1 13
  </code></pre>
  <p><strong>Checkmate in 3 moves. AP</strong></p>
  <p>In the light version, it's just an idea (no balance calculation is needed), in the second one, a pinch of retro is added: to prove that the a5 pawn does not have the last move, a balance calculation is needed.
  The solutions are almost the same.</p>
  <p><strong>Checkmate with white:</strong></p>
  <ol>
  <li>Nf6+? exf6 (only in the hard version)</li>
  </ol>
  <p><strong>1. Nxg7+ Kf8 2. Qf2+ Kg8(Kxg7) 3. Qf7#;</strong></p>
  <p><strong>1. ... Kd8 2. Qb6+ Kc8 3. Rxh8#</strong> (in the hard version 1. ... Kd8 2. Qb6#)</p>
  <p><strong>Checkmate with black</strong> (they declare that they do not have the last move preserving castling and the move passes to them):</p>
  <p><strong>1. 0-0+ (AP) Nf6+(f4) 2. Rxf6(f4)+ Qf2(Ke1) 3. Rc1#</strong> (In the light version 3. Ra1#)</p>
  <p><strong>Do I understand correctly that black checkmate here, and white checkmate is invalidated?</strong></p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-06-20T18:33:52.983Z
Comments.Text: Semi off-topic and probably a move to chat; if you've Discord, we've a chess server group for composing and such. Asking there also will help. There is also Matplus.net, but there does seem to be some blockage for newer accounts there recently.
Comments.UserDisplayName: Rewan Demontay
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-06-20T18:36:02.617Z
Comments.Text: Also, if there isn't en passant involved, it's not called AP. Castling logic alone is differently named. See https://www.janko.at/Retros/Glossary/Castling-and-En-passant.htm
Comments.UserDisplayName: Rewan Demontay
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-06-20T18:42:13.887Z
Comments.Text: On Mat Plus, new accounts are not blocked. You can have it, and you can even write something for a while. But after a while it is deleted because the registration has not been confirmed. And the registration has not been confirmed because the letter in which it should have been done is not sent to the specified mailbox.
Comments.UserDisplayName: Элси Ринген
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-06-20T18:58:24.440Z
Comments.Text: "Also, if there isn't en passant involved, it's not called AP. Castling logic alone is differently named."
  You're a little out of touch. The one you described is AP (Type Petrovic). Here we have a different type of AP (Type Keym for white, applied by black).
  It is useless to look for this in the "Corner of RA". There is definitely no such option there.
  I have never encountered this type of task at all. That's why I'm asking, is everything right here?
Comments.UserDisplayName: Элси Ринген
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-06-20T19:07:21.713Z
Comments.Text: And indeed. Would I ask a question, the answer to which is here: https://www.janko.at/Retros/Glossary/Castling-and-En-passant.html
  I have read that article both inside and out and I know it practically by heart.
Comments.UserDisplayName: Элси Ринген
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-06-20T21:04:52.323Z
Comments.Text: Ah sorry, my bad. Yeah I'm definitely out of touch here on the conventions.
Comments.UserDisplayName: Rewan Demontay
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-06-21T01:30:07.927Z
Comments.Text: I do not understand 0-0. Doesn't Rf8 suffice?
Comments.UserDisplayName: user58697
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-06-21T07:23:00.790Z
Comments.Text: I don't get it. Castling would be illegal if Black had made the last move, but so would Rf8 or any other move by Black.
Comments.UserDisplayName: bof
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-06-21T09:33:27.920Z
Comments.Text: "I do not understand 0-0. Doesn't Rf8 suffice?"
  In order to just checkmate, of course, it is enough. But in this case, when Black takes the move for himself on the basis that they have the right to castling, they simultaneously "promise" to castling in the decision process. Otherwise, they will not prove that they really have the right to castling and the move in the position has passed to black legally.
Comments.UserDisplayName: Элси Ринген
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-06-21T09:52:36.743Z
Comments.Text: If the move is in black's position, white's last move could be, for example, d5xNe6, and black before that Ng4-e6. And black retains the right to castling.
Comments.UserDisplayName: Элси Ринген
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-06-21T15:26:46.297Z
Comments.Text: I corrected the question, because it was not at all what I wanted to know.
  And I changed the task (otherwise they found a duality there).
  The old version of the task: 2b1k2r/Rp1pp1p1/4P1P1/pBN5/8/2P5/1PrPP1P1/5KQ1 - w
Comments.UserDisplayName: Элси Ринген
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-06-22T15:21:38.333Z
Comments.Text: Your light diagram has a couple of typos I think bKf8 should be on e8, and you need to add wPe6
Comments.UserDisplayName: Laska
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-06-22T15:37:49.547Z
Comments.Text: As a result, I removed both g7 and c7 in the light version. Light so light.
Comments.UserDisplayName: Элси Ринген
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-06-22T16:04:14.070Z
Comments.Text: Laska, I had some problems with the diagram and the e6 pawn was lost unauthorized (I did not immediately notice).
  I just take FEN from another editor, who is not very friendly with the local and always needs to be tweaked.
  Just in case, I will describe the arrangement of the figures here.
  White (10): Kf1, Qg1, Rh1, Nh5, PP. a3, b2, d2, e2, e6, g2.
  Black (4): Ke8, Ra2, Rh8, Pe7,
Comments.UserDisplayName: Элси Ринген
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2024-06-22T16:08:52.153Z
Comments.Text: And how the king appeared on one of the diagrams on f8, I do not understand at all. I definitely didn't plan this. :)
Comments.UserDisplayName: Элси Ринген
Tags: <problems><castling><retrograde-analysis><a-posteriori>
Title: Can the problem condition "A Posteriori Type Keym", which flips the player to move, also flip the player that delivers mate?
ThreadText: # Can the problem condition "A Posteriori Type Keym", which flips the player to move, also flip the player that delivers mate?
  
  (Asked by: username_0 on 2024-06-20)
  
  Again, I composed the task, but doubts crept in. Is everything really as I think it is?
  4k2r/4p3/4P3/7N/8/P7/rP1PP1P1/5KQR w - - 1 13
  
  2b1k2r/1p1pp1p1/4P3/p6N/6P1/2P5/1PrPP1P1/1B3KQR w - - 1 13
  
  Checkmate in 3 moves. AP
  In the light version, it's just an idea (no balance calculation is needed), in the second one, a pinch of retro is added: to prove that the a5 pawn does not have the last move, a balance calculation is needed.
  The solutions are almost the same.
  Checkmate with white:
  
  Nf6+? exf6 (only in the hard version)
  
  1. Nxg7+ Kf8 2. Qf2+ Kg8(Kxg7) 3. Qf7#;
  1. ... Kd8 2. Qb6+ Kc8 3. Rxh8# (in the hard version 1. ... Kd8 2. Qb6#)
  Checkmate with black (they declare that they do not have the last move preserving castling and the move passes to them):
  1. 0-0+ (AP) Nf6+(f4) 2. Rxf6(f4)+ Qf2(Ke1) 3. Rc1# (In the light version 3. Ra1#)
  Do I understand correctly that black checkmate here, and white checkmate is invalidated?
  
  **Tags:** problems, castling, retrograde-analysis, a-posteriori
  
  > **Comments:**
  > **username_1**: Semi off-topic and probably a move to chat; if you've Discord, we've a chess server group for composing and such. Asking there also will help. There is also Matplus.net, but there does seem to be some blockage for newer accounts there recently.  
  > **username_1**: Also, if there isn't en passant involved, it's not called AP. Castling logic alone is differently named. See https://www.janko.at/Retros/Glossary/Castling-and-En-passant.htm  
  > **username_0**: On Mat Plus, new accounts are not blocked. You can have it, and you can even write something for a while. But after a while it is deleted because the registration has not been confirmed. And the registration has not been confirmed because the letter in which it should have been done is not sent to the specified mailbox.  
  > **username_0**: "Also, if there isn't en passant involved, it's not called AP. Castling logic alone is differently named." You're a little out of touch. The one you described is AP (Type Petrovic). Here we have a different type of AP (Type Keym for white, applied by black). It is useless to look for this in the "Corner of RA". There is definitely no such option there. I have never encountered this type of task at all. That's why I'm asking, is everything right here?  
  > **username_0**: And indeed. Would I ask a question, the answer to which is here: https://www.janko.at/Retros/Glossary/Castling-and-En-passant.html I have read that article both inside and out and I know it practically by heart.  
  > **username_1**: Ah sorry, my bad. Yeah I'm definitely out of touch here on the conventions.  
  > **username_2**: I do not understand 0-0. Doesn't Rf8 suffice?  
  > **username_3**: I don't get it. Castling would be illegal if Black had made the last move, but so would Rf8 or any other move by Black.  
  > **username_0**: "I do not understand 0-0. Doesn't Rf8 suffice?" In order to just checkmate, of course, it is enough. But in this case, when Black takes the move for himself on the basis that they have the right to castling, they simultaneously "promise" to castling in the decision process. Otherwise, they will not prove that they really have the right to castling and the move in the position has passed to black legally.  
  > **username_0**: If the move is in black's position, white's last move could be, for example, d5xNe6, and black before that Ng4-e6. And black retains the right to castling.  
  > **username_0**: I corrected the question, because it was not at all what I wanted to know. And I changed the task (otherwise they found a duality there). The old version of the task: 2b1k2r/Rp1pp1p1/4P1P1/pBN5/8/2P5/1PrPP1P1/5KQ1 - w  
  > **username_4**: Your light diagram has a couple of typos I think bKf8 should be on e8, and you need to add wPe6  
  > **username_0**: As a result, I removed both g7 and c7 in the light version. Light so light.  
  > **username_0**: username_4, I had some problems with the diagram and the e6 pawn was lost unauthorized (I did not immediately notice). I just take FEN from another editor, who is not very friendly with the local and always needs to be tweaked. Just in case, I will describe the arrangement of the figures here. White (10): Kf1, Qg1, Rh1, Nh5, PP. a3, b2, d2, e2, e6, g2. Black (4): Ke8, Ra2, Rh8, Pe7,  
  > **username_0**: And how the king appeared on one of the diagrams on f8, I do not understand at all. I definitely didn't plan this. :)  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_4 on 2024-06-21. Score: 2
  
  It’s not really a matter of “correctness”. This is clearly not an orthodox problem. The issue is more whether the stipulation is “fair” and “elegant”.
  
  And I think it probably is fair. The problems are simple enough that the trick with the stipulation is guessable. I much prefer the second "heavier" version over the "lighter" one, although I haven't rechecked the retro play. I trust that the logic which worked in the earlier version works again.
  
  A alternative is to add the word "Who?" to the stipulation, indicating that the solver has to figure out who is the mater. But this makes the problem less elegant.
  
  Given that Black can unilaterally seize the move by immediately castling, White cannot prevent it. So the question becomes: what can #3 mean? Lateral thinking gives the answer.
  
  The basis principle of AP is clear: that executing castling can "prove" that other entangled rights are enabled. However the idea has not been formalized. Areas of complication include: (1) extension of the idea from RS (where it originated) to PRA (2) handling of information from multiple twins (3) AP Prioritat, and what suffices as a refutation (4) interaction with other conceits (such as here the reversal of player delivering the mate). There is no single agreed perspective on all of these, even amongst the experts. In the absence of unanimity, we should welcome the diversity, and acknowledge that your problem finds a unique place in this merry throng.
  
  The forward play is much better than your earlier dualed version. The checking keys are still defects, but may be difficult to avoid. I think the problem is still of publishable quality (except that it has been self-published here in chess.se). If you could find a matrix for your idea that avoids the checking keys that would be even more impressive.
  
  > **Comments:**
  > **username_0**: In my opinion, here (1. exd7+ Kf8) move 1. ... Kf8 is not defensive, because white is directly threatening 2. d7xc8=Q# and only Bxd7 and Kd8 are defensive moves. And the Kf8 move is kind of half cooperative.  
  > **username_4**: @ЭлсиРинген the notions of threat & defence only apply with a non-checking key! So Popeye treats all the Black moves Bxd7, Kd8 & Kf8 as equally valid options, the last being dualed.  
  > **username_0**: Checkmate in 2 moves (Who?) AP.  In my opinion (Who?) This is a bad idea. This will change the initial condition "by default, the move in white's position" to "whose move in the position is unknown".  This will create such confusion: white can, if black does not apply AP; black can, by applying AP; black can, without using AP (there is also a dual). Removing AP from the task is also not good: two answers and one with a dual.  
  > **username_0**: "This is the silly idea of A Posteriori Type Keym."  Perhaps it is better to make sure that white does not have a checkmate at all in two moves and the ability to checkmate black is the only way to complete the task?  
  > **username_4**: There is a difference between who moves first and who delivers the mate. halfduplex flips both of them. Who? flips the mate delivery. But this is not quite certain I agree. I think that with the AP folk will get to the right answer, but without it’s not clear. I don’t like stipulations which require narrow semantics interpretations but sometimes it’s difficult to avoid them without being clunky. Up to you  
  > **username_0**: I didn't argue with Popeye. I redid the Checkmate task in three moves. I don't like duals.  
  > **username_0**: To be honest, the idea of a pawn check on the first move seemed dubious to me from the very beginning.  
  > **username_4**: Rarely have I had to write an answer so many times in response to a changing question, for one measly upvote! :-)  
  > **username_0**: About the last paragraph of the answer. In my opinion, neither white nor black can avoid the check on the first move here. Otherwise, the other side will immediately torture you with their checks.  
  > **username_0**: I didn't quite understand the passage about AP not being formalized. As far as I know, AP has a clear formulation: "If the right to castling is required to solve a problem, then castling must be performed during the solution process, regardless of whether it is necessary for the solution or not." And all the tasks I know fall under this formulation.  
  > **username_4**: I've edited my answer to address the last two comments by Elsie  
  
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  ### Answer by username_0 on 2024-06-24. Score: 2
  
  Colleague username_4 suggested considering the issue in the plane of correctness and elegance. I agree with this statement of the question. And I will try to describe my vision.
  1. Correctness
  Tasks in which the parties have any special rights in the initial position (en-passant, castling), as a rule, may have different versions of the game in the past. There are usually two of them, but there may be more (as far as I know, five at most).
  And there are two methods for solving such problems:
  A) divide the problem into two parts with a different game in the past and solve both parts separately (together you will get one complete solution);
  B) choose one of the two options in the past by making an evidentiary move (this is always castling).
  Option B) is simple, has a clear name RS (Retro Strategy), everything is simple with it.
  Option A) is more complicated. There is a constant confusion with PRA (partial retroanalysis). The PRA uses the same method (dividing the task into parts based on different rights in the initial position), but the PRA Convention has a bunch of restrictions (there must be at least two special rights, they must be dependent on each other, etc.). Therefore, for cases of different games in the past, but not falling under the PRA Convention, it is better to use another name. I suggest RV (retro versions), but you can do any other. It's not about the name.
  If we consider the tasks of AP (A Posteriori) by type, then there are two past ones in Petrovic type:
  a) white has the right to en-passant and has the right to castling;
  b) whites have neither one nor the other right.
  There are also two previous ones in AP (Keym type, white):
  a) white has the right to move in position, but there is no castling;
  b) black is in position and white has the right to castling.
  In both cases, white cannot complete the task in both versions of the past and cannot complete it in the default version of the past, but can complete the task in another version of the past. And they only need to prove it by making a castling. The only difference between AP and simple RS is that we choose an option, not just by making a castling (the choice of the past here happens automatically), but first we choose the past, and then, as proof of the choice, we castling later.
  It is important here that in both cases white has the right to choose: they can leave the option that goes by default; they can choose another one. Black cannot influence white's choice in any way.
  The AP case is more interesting (Keym type, black).
  There are also two previous ones here:
  a) a move in white's position, black does not have the right to castling;
  b) a move in black's position, black has the right to castling.
  But it is important that black now has the choice of an option from the past and they can choose any one. Therefore, white needs to beat black in both ways to solve the problem.
  If in at least one variant white cannot complete the task, in the usual case it is the unsolvability of the task, marriage.
  And the solution to the problem here can only be saved if black completes the task instead of white. Then the problem will have a solution and it will be the only one, because it was performed by a party who had the opportunity to choose options from the past.
  By itself, completing a task with blacks instead of whites is not a new thing. In half of the "Checkmate in 1 move" tasks, black is checkmated.
  Is there a difference between the tasks "Checkmate in 1 move" and "Checkmate in 4 moves"? In my opinion, no. All these are tasks of the same type "Checkmate in N moves".
  Only the justification for completing the task for black is slightly different. This is usually just a retroanalysis of the position, where it turns out that the position during white's move is illegal. Here, black proves the illegality of the position during the course of white, using the opportunities provided by the AP agreement.
  That's how it is...
  2. Elegance
  The task was conceived simply as a joke. However, according to the rules (and not as it sometimes happens, where the rules must first be thought out ... :)). It was done in a hurry. Just to test the idea. Apply the same technique in the type of Case for blacks that is usually used by whites.
  And I completely agree with Lask's colleague that shahi on the first move is "not good at all."  And for a long time it seemed to me that it was impossible to get rid of them with such a statement of the question. But it turned out that it was possible. At least on the first move (and white will have no time for checks at all).
  4k2r/Np4p1/RR1pPB2/4p3/N1P5/p1p1P1P1/rP2P1PP/5KQ1 w - - 1 13
  
  Checkmate in 4 moves
  White does not have the opportunity to check on the first move at all. And considering that black has the opportunity to put two checks at any pause, white needs a checkmate in two moves. And he is!
  1. Nc6 Ra1+ 2. Kf2 Rf1+ 3. Kxf1(Qxf1)
  3. ... bxa6 4. Rb8#; 3. ... gxf6 4. Ra8#
  But this is a fiction and a mirage, because by a strong-willed decision, black takes the move for himself.
  1. 0-0 (I suffered for a very long time so that, in addition to 1. 0-0, I could just pass 1. Rf8. Otherwise, it would just be a simple duplex).
  Black threatens with a simple mat in two moves.
  
  ... Kf2 (e4, e7) 2. Rxf6 ... 3. Ra1#
  
  ... Ke1 2. Ra1 ... 3. Rxf6#
  
  
  The most white can do is delay the inevitable by one move.
  1. 0-0
  1. ... Qf2 2. Ra1+ Qe1 3. Rxf6+ Kg1 4. Rxe1#
  1. ... Nxc3 2. Ra1+ Nb1(d1) 3. Rxb1(d1)+ Kf2 4. Rxf6#
  1. ... bxc3 3. Ra1+ Rb1 3. Rxb1+ Kf2 4. Rxf6#
  
  
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