06 April 2012

Retro mix

Today, I have two retro chess problems for you. Enjoy!

T. R. Dawson
Cas, 1922
[k6n/P3ppNp/pPK3pP/2p5/1pP3P1/6Pp/4PP2/8]
Add one man so that White to play can mate in two

We know that White is to move in the diagram. Obviously, something must be wrong, since White already has a mate in two by 1. Ne8 and 2. Nc7. So, it seems the addition of a further piece is unnecessary.

Let's start the retro-analysis to find out what's wrong. White has made at least five pawn captures on the kingside. As only six black men are missing, there's at most one capture left for White on the queenside. This means that the white pawn on b6 has never made a capture. Otherwise, that required another capture due to the pawns on a7 and c4, respectively.

As a consequence, the black pawn on b4 has made a capture which implies a second pawn capture by Black on the queenside. Together with the four on the kingside, all black captures are resolved. Therefore, the missing piece must be black. This means that actually only five black men are missing and this fits exactly with what we already found out.

Let's check where White captured. The h6-pawn started from d2 and took pieces on e3, f4, g5 and h6. The h3-pawn must have arrived via the capture g4xh3, so the history of moves in the bottom right comer must have been either g4xh3, then g2-g4 and h2xg3, or g4xh3, then h2xg3, g3-g4 and g2-g3. In either case, White captured on g3. A closer look reveals that all White captures took place on black squares. So, the black bishop from c8 hasn't been taken by White. This is the piece that is to be added.

Where can we put the bishop without disturbing White's mate in two by 1. Ne8? There are just three candidate squares, namely a2, e8 and h5. Not e8, because Black has no previous move. And h5? If so, Black's last move must have been b5-b4 or a5xb4. As White hasn't made a pawn capture on the queenside, the following sequence must have occurred: WPb2 to b5 or b6, Black's a-pawn captured to go behind the b6 pawn, WPa2 to a7 and finally Black played b7xa6. So the last move could not have been a5xb4, since this happened before the white pawn advanced to a7. Therefore, it must have been b5-b4, but in this case the two Black queenside pawn captures took place at b5 and a6. These squares, like e6, f5, g4 and h3, are white squares. Black could not have captured White's queen's bishop.

We have to add a black bishop on a2.

R. Kofman
Shakhmaty Bulletin, 1958
[4k2r/1pp2p2/p3pP1p/8/1P6/2pR2pP/2PP1PP1/2KR4]
White retracts his last move and then mates in 3

If Black was unable to castle, White could mate in two from the diagram by 1. d2xc3. So, we must retract a move that proves that Black cannot castle. We might try taking back 0-0-0. Then White's king has never moved. This means that the white rook d3 is a promoted pawn. If the pawn promoted at g8 White must have made seven pawn captures, which is too many. The promotion must have taken place at a8, b8, c8 or d8, or f8. In each case the black king must have moved, thus 0-0 is illegal.

We still have the task of mating in three, so we must prevent gxf2+. This can be accomplished by playing 1. 0-0-0! (threat 2. dxc3), the very move we just took back. Funny!

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