Pal Benko's final problem

Question

EDIT: Link added

One of my chess heroes, Hungarian GM Pal Benko, is no longer with us. He overcame many difficulties in his early life to live one which was rich and full, and reached the age of 91 with his faculties undimmed. I love the clarity and variety of his problems and puzzles, and am moved by an article by another Hungarian GM, Susan Polgar, to relay his new, final composition as a tribute. First I will quote Polgar verbatim, and then give some technical comments.

This was his final request to me, to share this Help Mate Composition with the Chess World!

This is the last chess composition Pal Benko shared with me when I visited him and his wife at their home in Budapest last week.

This is a a Help Mate Composition! From the starting position, White starts the game and checkmates Black by En Passant on the 9th move!

In addition, the game MUST include all the SPECIAL chess moves (at least from one side) such as Pawn Promotion, Castling, En Passant (in addition to the final checkmate), and Discovered Check. There is only one possible solution (according to Benko himself).

He was very proud of this Help Mate Masterpiece and asked me to share it with all of you! This was his final request to me.

Enjoy!

(1) This kind of problem is known as a "synthetic", and can be very hard to solve, "a real test of chess imagination", as the veteran chess columnist Len Barden would say. It's not a proof game, but a problem with constraints.

(2) It contains a "Valladao": i.e. castling + promotion + en passant. But beyond that there is a fourth thematic move here (Discovered Check) and the constraint that these four thematic moves should be played by the same player.

(3) There is a second en passant, which delivers mate. It seems consistent with the wording that this second en passant might be the thematic Discovered Check, in which case the player of all thematic moves would have to be White. However, then White has 5 moves for promotion including e.p., 3 for second pawn, 1 for 0-0 and maybe 2 to move B&N for 0-0. That makes 10 which seems to be too many. If it's Black doing the thematic stuff: 5 for promotion including e.p. which can be discovered check, 1 for 0-0, 1 for pawn to be eped, and 2 to move B&N for 0-0. That's 9 again too many. So kB or kN must have been captured on its starting square and then got right out of the way. Maybe N captures kN and then after moving is captured by bB? (EDITED for clarity)

(4) Normally in a proof game with e.p., one can reason by uniqueness that the double pawn move must have been blocking a check, because otherwise the move might as well have been a single pawn move. But here in this thematic synthetic, that constraint is not present.

And beyond that I currently have no idea of the solution! Good luck!

Answer 1

No answers here, and I haven’t seen any solution in the rest of the world. So I thought I would post a work-in-progress here.

First let’s take a baby step. Which player is the one who has all these adventures?

Suppose that it’s White. Then the pawn which moves in W9 (White’s 9th move) makes 3 moves to reach the sixth rank. In addition, another pawn makes 5 moves to promote. This must have been the same pawn which executed the earlier en passant. And finally there is the castling. That exhausts 9 moves. So that means that the two or three officers which blocked the castling has to have been cleared out by Black helpful captures. Black made 2 pawn moves for en passant purposes, so that means 6 moves remain for raiding. It can’t have been a promotion because that uses 5 moves and to capture the neighbour would use the 6th, implying the promotion was to R or Q which would disturb his majesty wK. And clearly it wasn’t original R or Q which captured the officer next to wK. Capturing with N requires 4 moves to reach and 1 to retreat. So the other white officer can’t be captured. So by elimination the pieces must have been captured by black bishops. Each bishop requires 2 moves to arrive and one to run away, but in addition black’s first move did not contribute to any of this.

So we have proved that White was not the player who had all the adventures. It must have been Black.

Let’s see how the budget works out if Black is the protagonist. Black promotes, taking 5 moves including a promotion. There is 1 for castling and 1 for B8 pawn move prior to e.p. So 7 out of 8 moves are accounted for.

On the other hand White has 1 move to feed the Black e.p., 3 for the pawn which executes the White e.p. That’s 4 out of 9. But White is required to go capture at least one of the Black bank rank officers. (Another might move away using the Spare Black move.)

Could Black have castled on the queen side? In this case white must have captured two Black officers at home. With only 5 moves this can’t have been pawn or knight. Two bishops require too many moves to escape after. So at least one raider must have been R or Q. This means that the raider would capture N&B, while bQ shielded bK, and both later ran away. Can’t

Can’t quite exclude this one corner case right now, although it seems unlikely. The other, easier possibility is that Black castled on kingside. If Black did castle kingside then the earlier argument about White castling applies. So one of the two Black officers must run from the back rank.

Therefore in either case we have exhausted the Black moves, and can conclude that bK did not move after castling and was mated on g8 or just possibly on c8. So the final e.p. was discovered check. Since the castling rook doesn't move after the castling is complete, the discovered checkmate can't just be for bishop/queen on the diagonal. It must be rook/queen checkmate on the file as the old e.p. double checkmate is only available if the king were on 6th rank.

That all seems reasonable: indeed some actual creative thinking maybe required to progress further!

Answer 2

If anyone still doubts that all of the special moves are impossible to achieve in just 9.0 moves, or 18 plies, I think that this should help. Here is a unique proof game in 8.5 moves, or 17 plies. This is the only possible sequence of moves to reach the final position in the prescribed time.

[Title "Enzo Minerva, Best Problems #36 10/2005, Proof Game In 8.5 Moves"]
[FEN ""]

1. e4 f5 2. Bb5 f4 3. Ne2 f3 4. O-O fxg2 5. e5 gxf1=B 6. Kh1 Bxe2 7. Qxe2 Kf7 8. Qc4+ d5 9. exd6+

Source:The Die Schwalbe Chess Problem Database