# Pal Benko's final problem

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!

• Susan Polgar's post Aug 28, 2019 at 21:17
• I will tend to this on the weekend, but some additions upfront: a) Actually no side is promoting AND castling! You made the proof for white yourself, but as black's last move is pawn to ?5 (allowing e.p.#), black also has not enough moves to both castle and promote. b) White has to make a minimum of 4 pawn-moves to mate and allow the second e.p. IF he is NOT promoting. Otherwise white has exactly 8 pawn- and 1 piece move. If it is possible to mate this way will be proven on the weekend. ;) However this scenario should even already be brute-forceable. I'll get back to you on the weekend! Sep 24, 2019 at 22:40
• Hi thanks for your response - it seems pretty clear that one side IS asked to promote and castle. That’s why I copied the exact words from Judith Polgar. The other side must be eliminating at least one of kB or kN on its home square. I have seen someone else on another site come up with a non-unique solution where the special moves were split between the two players. It follows this cannot have been Pal’s intended interpretation. Good luck! Sep 24, 2019 at 23:28
• On the 9th move it is provably impossible. Could it have been 19th move in the original problem and there was a typo in Susie's post? Dec 25, 2019 at 23:56
• You interpret " the game MUST include all the SPECIAL chess moves (at least from one side) " as "these four thematic moves should be played by the same player". But couldn't it mean that at least one player must have played each of these four special moves, even if they are not executed by the same camp ? Nov 4, 2021 at 14:41

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!

• good luck. my analysis showed it is impossible. 19 moves yes, but 9 no. Dec 31, 2019 at 14:50
• Well we’ll see Haha! Dec 31, 2019 at 17:12
• We will see if someone solves it. It is impossible to PROVE a negative but my analysis shows it cant be done. Maybe I missed something obscure that lets it happen. I still suspect it was a typo. Dec 31, 2019 at 17:16
• I think the phrasing of the problem is unfortunate: I suspect that the special moves do not all have to be by the same player, i.e. in addition to the final e.p. mate, there is somewhere in the game a castling, an e.p., a discovered check, and a promotion. Trying for a little while, it still feels sufficiently difficult that this may be the intended problem. Dec 31, 2019 at 18:08
• Well I want to go ahead with my interpretation until I find my own proof of failure. Dec 31, 2019 at 18:28

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+
``````
• But in Benko's problem a second en passant is required... Nov 4, 2021 at 14:42
• @Evargalo No? Only one en passant is needed as far as I can tell. Nov 4, 2021 at 17:43
• Benko's stipulations in the OP : "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." I understand that there is one en passant at some point during the game PLUS one at the final checkmating move. Nov 5, 2021 at 10:10
• I disagree, as it does not say "two en passants" specifically." It reads as one of each special move in addition to a discovered check (which more than likely is part of the en passant) Nov 5, 2021 at 13:32