Mate in 4 (Petrovic)

Originally posted by BigDoggProblem
Mate in 4 means Mate in 4. There should be no shorter solutions.

Ok, this is a little heuristic, and hence isn't a complete solution but...

Using proof by contradiction:
1/ Assume (for the sake of this mini-proof only) that en-passant is legal, and solution has mate in no less than 4.
2/ Find mate in 2
3/ Contradiction found, one of assumptions must be wrong
4/ Hence en-passant not legal.

This then means we have to find a mate in 4 which does not involve en-passant. Which is where I get really stuck - as do a lot of people by the look of this thread.

Originally posted by Zeddicus
Ok, this is a little heuristic, and hence isn't a complete solution but...

Using proof by contradiction:
1/ Assume (for the sake of this mini-proof only) that en-passant is legal, and solution has mate in no less than 4.
2/ Find mate in 2
3/ Contradiction found, one of assumptions must be wrong
4/ Hence en-passant not legal.

This then means ...[text shortened]... -passant. Which is where I get really stuck - as do a lot of people by the look of this thread.

I'm afraid you're hung up on an irrelevant point. As I've stated several times, you cannot just assume that en passant is legal.

Originally posted by BigDoggProblem
I'm afraid you're hung up on an irrelevant point. As I've stated several times, you cannot just assume that en passant is legal.

Not meaning to start an argument but I think you're missing my point entirely. I'm am not assuming it's legality, but simply asking the question:

Before working through any proof of en-passant, doesn't the fact that it's legality would enable mate-in-2 mean that it automatically can be discounted as being involved in the solution?

Ok, apologies I guess. I've discussed this with a lecturer who's a big chess fanatic, and now accept that Chess doesn't follow the same rules as pure mathematics - that a disproof of something (like I've done above), doesn't necessarily mean that you shouldn't also be able to prove it is true.

I must admit I'm still confused as to why, but never mind.

I'd just like to see the full, official solution to this problem. 🙁

Originally posted by Zeddicus
Before working through any proof of en-passant, doesn't the fact that it's legality would enable mate-in-2 mean that it automatically can be discounted as being involved in the solution?

No, it cannot automatically be discounted. Once you hit upon the means to prove that en passant is legal, you'll discover mate in 2 is no longer possible.

Originally posted by Zeddicus
Ok, apologies I guess. I've discussed this with a lecturer who's a big chess fanatic, and now accept that Chess doesn't follow the same rules as pure mathematics - that a disproof of something (like I've done above), doesn't necessarily mean that you shouldn't also be able to prove it is true.

I must admit I'm still confused as to why, but never mind.

I'd just like to see the full, official solution to this problem. 🙁

Refer to the last post on page 2 of this thread for the necessary retroanalysis. It proves that there are two possible realities for the position:

A) White can't castle, nor can he capture en passant.
B) White can capture en passant, and he still has castling rights.

The solution is:
1.dxc6ep! b5!
White has not yet proven that he has the right to play en passant on move 1, so it is an open question whether 2.d7 is checkmate or not - obviously, if an illegal move has been played in the past, all checkmates are null and void.
2.0-0-0!
The proof! White has just established that we're in reality B) above. This is in line with the FIDE Codex, which tells us that we may assume castling is legal unless provable otherwise.
2...Bb6 3.Nd7+ Ka7 4.b8Q#

I'm sure a lot of chess players won't be happy with the idea of A Posteriori proof - proof offered after the fact. However, there is no good alternative - too many nice chess problems would be ruined if castling could not be assumed legal. Same goes for retrograde problems involving a lengthy proof of the legality of en passant.

But what about the solution that involves neither e.p. nor castling?

Originally posted by Ian68
But what about the solution that involves neither e.p. nor castling?

There isn't one.

Another example:

White to play and win

1.d7! Kc7 2.d8Q+! Kxd8 3.0-0-0+ wins the Rook and the game.

As in Petrovic's problem, there's no point to asking, "but what about the solution where White can't castle?" If White cannot castle, he cannot win.

Originally posted by BigDoggProblem
There isn't one.

You're right, I had the knight on the wrong square. 😳

I also re-read your solution and discovered it makes no sense whatsoever. You say castling is assumed legal if it cannot be proved illegal. It cannot be proved illegal in that position so is therefore assumed legal. En passant can only be legal if castling is legal, and it has already been established that for the purposes of this puzzle castling is legal. Therefore 1 dxc6 can be assumed to be legal and 2 d7 is checkmate.

Originally posted by Ian68
You're right, I had the knight on the wrong square. 😳

I also re-read your solution and discovered it makes no sense whatsoever. You say castling is assumed legal if it cannot be proved illegal. It cannot be proved illegal in that position so is therefore assumed legal. En passant can only be legal if castling is legal, and it has already been established t ...[text shortened]... is puzzle castling is legal. Therefore 1 dxc6 can be assumed to be legal and 2 d7 is checkmate.

Completely wrong. Congratulations on missing the whole point of the problem even after being given the answer.

There are two assumptions at play here. One is that en passant is assumed illegal, the other is that castling is assumed legal.

You claim that the assumption that castling is legal ought to override the assumption that en passant is not legal. Why? Isn't it equally possible that White has neither castling rights nor en passant rights on move 1? Without actually castling in the course of play, how do you eliminate this possibility from consideration?

Originally posted by BigDoggProblem
Completely wrong. Congratulations on missing the whole point of the problem even after being given the answer.

There are two assumptions at play here. One is that en passant is [b]assumed illegal, the other is that castling is assumed legal.

You claim that the assumption that castling is legal ought to override the assumption that en ...[text shortened]... ually castling in the course of play, how do you eliminate this possibility from consideration?[/b]

The conditions you listed stated that the legality of castling takes precedence over the illegality of en passant, this is not something I have claimed. Also, castling as part of a solution does not prove castling was legal, only analysis of the position can do that.

Originally posted by Ian68
The conditions you listed stated that the legality of castling takes precedence over the illegality of en passant, this is not something I have claimed. Also, castling as part of a solution does not prove castling was legal, only analysis of the position can do that.

"The conditions you listed stated that the legality of castling takes precedence over the illegality of en passant, this is not something I have claimed."

This gives you the right to prove en passant legal by castling and nothing more. You're still having trouble grasping the fact that, when ep and castling rights are linked, assumptions can work both ways. If castling rights did not take precedence over ep, then one could rightly argue that the assumed illegality of en passant also nullifies castling rights, since the two rights are linked.

"Also, castling as part of a solution does not prove castling was legal, only analysis of the position can do that."

Wrong again - castling cannot be proven legal in the overwhelming majority of problems. A proof game can start 1.Nf3 Nf6 2.Nc3 Nc6 3.Rg1 Rg8 4.Rb1 Rb8 followed by the return of all the pieces to their homesquares. All castling rights have already been lost. In a forced-mate problem, it's virtually impossible to prove that this didn't occur at the start of the game.

This is precisely why castling must be assumed legal - without that assumption, we can throw away 99% of the problems involving castling. The only exception are problems where the beginning of the game is controlled by the composer, such as Proof Games.

Originally posted by BigDoggProblem
"[b]The conditions you listed stated that the legality of castling takes precedence over the illegality of en passant, this is not something I have claimed."

This gives you the right to prove en passant legal by castling and nothing more. You're still having trouble grasping the fact that, when ep and castling rights are linked, assumptions can ...[text shortened]... blems where the beginning of the game is controlled by the composer, such as Proof Games.[/b]

1. You are having trouble grasping the meaning of the word precedence.

2. I should have said "castling as part of the solution does not prove that the conditions in which castling can be assumed legal have been met, only analysis of the position can do that."

Originally posted by Ian68
1. You are having trouble grasping the meaning of the word precedence.

2. I should have said "castling as part of the solution does not prove that the conditions in which castling can be assumed legal have been met, only analysis of the position can do that."

In response to point 1:

http://m-w.com/dictionary/precedence

"precedence" means "priority of importance". That's the meaning I intended.

In response to point 2:
Castling is always assumed legal in all chess problems conforming to the FIDE Codex. There are no conditions which need to be met.

Originally posted by BigDoggProblem
Castling is legal, unless it can be proven illegal.

Originally posted by BigDoggProblem
Castling is [b]always assumed legal in all chess problems conforming to the FIDE Codex. There are no conditions which need to be met.[/b]

Now you are contradicting yourself.