# Mate in 4 (Petrovic)

BigDoggProblem
Posers and Puzzles 06 Oct '06 22:02
1. BigDoggProblem
06 Oct '06 22:02
N. Petrovic

#4
2. 07 Oct '06 12:50
Originally posted by BigDoggProblem
N. Petrovic
[fen]1k3N2/bP5p/pp1PPPP1/2pPBbRB/3pppp1/8/PP6/R3K3 w Q - 0 1[/fen]
#4
I'm not entirely sure if my solution is correct, but I'll give you my best try.

1. d7+ Kxb7
2. d8=Q Bb8
3. Qxb8#

2. ... Bxe6
3. Qc7+ Ka8
4. Qc6#

I just looked at the problem right after I woke up so I probably missed something.
3. 07 Oct '06 14:53
I guess the key is en passant capture, legality proved by a later castling. I'll try to prove it later...
4. 07 Oct '06 16:00
If black's last move was a single pawn step then white's last move was by K or R (I didn't prove this completely yet), therefore white can't castle.
So if white can castle then black's last move was a double pawn step, and white may capture e.p.
Solution:
1.d:c6 d3 2.0-0-0 d2+ 3.R:d2 B:e6 4.d7#
1...b5 2.0-0-0 Bb6 3.Nd7+ Ka7 4.b8=Q#
White's castling is an a-posteriori proof that the e.p. capture was legal.
5. BigDoggProblem
07 Oct '06 19:31
Originally posted by hypothetical
I'm not entirely sure if my solution is correct, but I'll give you my best try.

1. d7+ Kxb7
2. d8=Q Bb8
3. Qxb8#

2. ... Bxe6
3. Qc7+ Ka8
4. Qc6#

I just looked at the problem right after I woke up so I probably missed something.
Why not 2...a6, trying to escape on the light squares?
6. 07 Oct '06 19:39
Originally posted by BigDoggProblem
Why not 2...a6, trying to escape on the light squares?
I knew my answer was probably too simple. ðŸ˜³
7. 07 Oct '06 20:14
I am somewhat unsure of the legality of the position. White has made 5 captures 4 with the h-pawn to d6, and one with the c-pawn at b7 and Black is missing 5 pieces (Q, 2R, 2N) on the other hand White is missing only a Queen and Knight, so how did the Black pawns at e4 to g4 have made it behind their opponents? Other than that, I still cannot see a mate in 4. Will think some more, though...
8. 07 Oct '06 20:371 edit
If black's last move was c6-c5 then white's last move was c4:d5, a move by K or a move by R. But c4:d5 is not possible - there are only 5 black pieces missing. so if black's last move was c6-c5 white can not castle. Equivalently, if White can castle then black's last move was c7-c5 so white may capture e.p. on the key move. This justifies my solution posted above.
9. 08 Oct '06 09:13
Originally posted by David113
If black's last move was c6-c5 then white's last move was c4:d5, a move by K or a move by R. But c4:d5 is not possible - there are only 5 black pieces missing. so if black's last move was c6-c5 white can not castle. Equivalently, if White can castle then black's last move was c7-c5 so white may capture e.p. on the key move. This justifies my solution posted above.
Think I understood it this time. So you are also using the fact that it HAS to be mate in 4 to prove that castling is legal? (as after e.g. Rb1-a1 c6-c5 there is no mate in 4?)
Otherwise I don't know why those moves couldn't lead to the current position and we'd have to find mate in 4 without castling.
10. 08 Oct '06 10:10
No.
I don't use the fact that the problem must have a solution.
The general rules are:
1. e.p. capture is illegal unless it can be proved legal;
2. castling is legal unless proved illegal.
In our case, rules 1 & 2 contradict each other, since by rule 2 castling is legal, and that implies the e.p. legality; but by rule 1 the e.p. is illegal. The rule in such case is that white may capture e.p., but only if later he actually castles; the castling is an a posteriori proof that the e.p. capture was legal. Weird ðŸ™„
11. BigDoggProblem
08 Oct '06 17:09
What's missing is a good explanation of the retro play.
12. 08 Oct '06 22:47
Originally posted by David113
No.
I don't use the fact that the problem must have a solution.
The general rules are:
1. e.p. capture is illegal unless it can be proved legal;
2. castling is legal unless proved illegal.
In our case, rules 1 & 2 contradict each other, since by rule 2 castling is legal, and that implies the e.p. legality; but by rule 1 the e.p. is illegal. The rule in ...[text shortened]... tually castles; the castling is an a posteriori proof that the e.p. capture was legal. Weird ðŸ™„
don't tell me someone actually took the time to make an official rule like that!
13. BigDoggProblem
08 Oct '06 23:20
Originally posted by aginis
don't tell me someone actually took the time to make an official rule like that!
Of course they did. There are many chess composition magazines and tournaments out there; standards are needed, just like the rules that govern Chess, the Game.
14. 10 Oct '06 05:19
Originally posted by David113
No.
I don't use the fact that the problem must have a solution.
The general rules are:
1. e.p. capture is illegal unless it can be proved legal;
2. castling is legal unless proved illegal.
In our case, rules 1 & 2 contradict each other, since by rule 2 castling is legal, and that implies the e.p. legality; but by rule 1 the e.p. is illegal. The rule in ...[text shortened]... tually castles; the castling is an a posteriori proof that the e.p. capture was legal. Weird ðŸ™„
The position itself is illegal, so any claims on the legality of e.p and castling and last moves have nothing to be based upon. To prove something legal is to construct a legal sequence of moves that lead from a legal position to the position in question. Since this is impossible, I'd say this whole problem is something of a misconception.
15. BigDoggProblem