A classic retractor

Solutions

We start with a letter that gives the full solutions in exemplary fashion:

Thomas J. McElmurry, Champaign, Illinois, USA
At first glance, these puzzles are quite surprising. How can a simple translation of the pieces by one, two, or three ranks alter the character of the solution? In none of the diagrams is the black king on the first or eighth rank, so we cannot use the edge of the board as a mating net. Apart from castling, which is obviously not possible here, the only rules of chess which change from rank to rank are those involving pawns -- namely, the initial double step, capturing en passant, and promotion. Therefore we shall focus on the pawns in these diagrams.

Looking at any of the diagrams, we can see that if White can manage to remove both of his pawns from the rank occupied by Black's king, then the white rook on the a-file will deliver mate, provided that one of the white pawns, in taking back its move, can protect this rook from the black bishop without leaving behind an "uncaptured" black piece to block the check. We find that this is possible in three of the four cases; the solutions are as follows.

Retractor by M. Adabashev, "64" 1938

In Diagram A, White has just played 1.Pc2-c4. He takes this back, leaving a pawn on c2 to block the path of the bishop, and instead plays 1.d5 mate.

In Diagram B, White has just played 1.Pb4xc5 in response to Black's previous move, Pc7-c5. He takes this back, leaving a pawn on b4, to block the path of the bishop, and a black pawn on c5, which could block his rook's mating attack. He can remove this obstacle in only one way: he plays 1.dxc6 e.p. mate.

In Diagram C, White has just played 1.Pbxc6 e.p. in response to Black's previous move, Pc7-c5. He takes this back, leaving a pawn on b5, to block the path of the bishop, and a black pawn on c5, which will not obstuct the mate. He then plays 1.d7 mate.

In Diagram D, the only way that White can take back a move and protect his rook from the black bishop is to take back 1.Pbxc7. However, this would leave a black piece on c7 which White could not remove by advancing the d-pawn. We conclude that White can give check with his a7-rook only by leaving it vulnerable to capture by the black bishop. How then can we wriggle out of this dilemma? A double attack will do nicely. White's last move was not a capture, but rather the simple advance 1.Pc6-c7. He takes this back and instead plays 1.d8=N mate, and the black king can escape either from the rook or from the knight, but not from both.

This puzzle, while not terribly difficult, was quite enjoyable. Once I determined that I needed to focus on the pawns, the necessary moves in each case were easy to find. Nonetheless, each diagram is an elegant puzzle in its own right, and the existence of four distinct unique solutions is surprising, and rather beautiful.

Jens Stein (aka Chuenthe on playchess), Germany
1. Regretting my blunder and thinking of Fischer I take back the stupid c2-c4 and play d4-d5# instead (Thanks Bobby).

2. Mumbling the words „Oooops, I didn’t know pawns can move like that“ I put the c-pawn back on b4 (b4xc5) and move dxc5 e.p. # instead. (Blacks last move was c7-c5)

3. This mistake is really quite easily explained. Having learned the funny move in the previous example, I thought it to be a real killer so I answered blacks c7-c5 with bxc5 e.p. thus successfully employing the newly learned rule (so it was not a mistake at all, really). I was so intent on this that I didn’t see the simple d6-d7#.

4. I know I should have moved d7-d8N# instead of c6-c7, but this was done in the true sense of Fischer. He always wanted to annihilate his opponents ego and I do love to play two queens and a rook against Juniors stupid bishop. Let him squirm, hahaha. I have disabled his ability to resign. Do you think I’ll let him off with a simple mate now? Ha, no way! He has humiliated me with his stupid tactics once too often.

Thank you so much for a very nice site.

Brian L. Galebach, Columbia, MD, USA
This is quite an unusual and interesting type of problem. Unlike a lot of chess problems, which I find to be mainly trial and error, and thus boring, these retractors make you really think logically.

Daniel Nadasi, Woollahra, NSW, Australia
The solutions took me about 20 minutes to find. The essential thought behind it was that if the rooks moved, I would probably be able to find a solution that wasn't unique to each position. But of course the bishop is attacking my mating rook (if the rooks don't move), so I tried to find a way of taking back pawn moves in order to block the bishops attack. This led fairly quickly to the solutions.

Vincent L. Fish, Somerville, MA, USA
Great puzzle! You have some of the most clever and inventive problems on your site, and this is one of the few I've been able to solve (hopefully, correctly). For some reason, part B seemed hardest, even after I had figured out the en passant trick to part C. Maybe having two possible ways to capture was just too much of a mental block.

Joshua Green, Phoenix, AZ, USA
These problems seem to violate normal retrograde standards in that White retracts a move which cannot be proven to have been his/her last. The solver must assume the existence of a solution to find it. Perhaps a better stipulation would be "White has just moved but could have checkmated Black. How?" At any rate, this is a remarkable problem. It's particularly nice that each wP gets to "make" an e.p. capture.

I'm always happy when there are new problems and/or tactical exercises on your site. Yours is one of the websites that I visit on a daily basis. The news you print on the frontpage is usually interesting. The Online Database has proven very useful to me. However, I would suggest that you merge the Download and Support sections. If someone is looking for, say, a program patch, it isn't always obvious which section it would be in. Overall, keep up the good work!

Navin Sawalani, Singapore
Great site btw. I visit it at least once every single day! I especially love the fact that it is updated every day. The reports are excellent with plenty of pictures and diagrams (i'm pretty sure pics and diagrams go down very well with the majority of viewers of this site). The puzzles are excellent. I especially like the tactical puzzles u guys extract from the tournaments and also the Christmas puzzles (for all the years, 1999-2002), although truth be told I have some difficulty solving some of the christmas 2002 puzzles. The coverage of important tournaments are great! Some site just present the games in pgn and nothing more, but u guys actually produce full illustrated reports; far more entertaining than just the moves. Kudos to Mig Greengard as well for his many contributions. Great site guys! Keep up the good work and u guys definitely have my support!

Phillip Monk, Adelaide, Australia
These types of puzzles illustrate the "quantum-mechanical" nature of chess -until White decides whether to capture en passant, Black's pawn is spread between two states, simultaneously inhabiting the 5th and 6th ranks! I'd convinced myself the second puzzle was impossible until I realised that it hinged on Black's c-pawn being in two places at once!

Brian Stewart, San Jose, CA, USA
The first and last variations weren't hard. I struggled with the other two, until I remembered the example problem you gave that involved the ep capture. Then it was just like, "Oh. Duh." Good exercise though, and a lot less tortuous than a helpmate! ;)

David Manning, Sherman Oaks, CA, USA
As always, I tremendously enjoyed the puzzles on your page. This time, I think I was actually able to figure them all out! It seems that the basic mechanism was to find a way to discover a check with the a-rook on Black's king while simultaneously preventing Black's bishop from capturing the a-rook. In the first three positions, this involved being creative with pawn pushes and en passant captures to block the bishop's line of attack. In the fourth position, the key was to create a discovered double check via an underpromotion.

Thank you for a pleasant Sunday diversion. I look forward to more puzzles in the future!

John Nolan, Research scientist, University of Oxford, England
What a fantastic puzzle! The fact that the vertical translations of the pieces result in four different and unique solutions suggests that movements of the pawns are critical: after all this is the only piece whose set of available moves can change depending on its vertical position (save kings and rooks when castling, which is clearly irrelevant here).

The winner

The prize, an autographed copy of Fritz, was won by Christoph Mattheeuws of Lima, Peru, whose name was selected by random from all the submissions with correct solutions.