# Can the problem condition "A Posteriori Type Keym", which flips the player to move, also flip the player that delivers mate?

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:

1. 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?

• 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. Commented Jun 20 at 18:33
• 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. Commented Jun 20 at 18:42
• "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? Commented Jun 20 at 18:58
• And indeed. Would I ask a question, the answer to which is here: 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. Commented Jun 20 at 19:07
• I do not understand 0-0. Doesn't Rf8 suffice? Commented Jun 21 at 1:30

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.

• 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. Commented Jun 21 at 11:05
• I didn't argue with Popeye. I redid the Checkmate task in three moves. I don't like duals. Commented Jun 21 at 15:52
• To be honest, the idea of a pawn check on the first move seemed dubious to me from the very beginning. Commented Jun 21 at 16:50
• 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. Commented Jun 22 at 16:37
• 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. Commented Jun 22 at 17:18

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.

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.

1. ... Kf2 (e4, e7) 2. Rxf6 ... 3. Ra1#

2. ... 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#