20 March 2011

Who's Missing

Don't worry, I am not going to write about the album of the same title. Or should I say I'm sorry? It's not that I would not like music by The Who. But I want to write about chess problems (and I will).

A certain type of retros asks you to add one or more pieces in a way yielding a legal position. There are different variations. You might know what and how many units to add. In other cases, you have no further restrictions and must find out yourself what is missing and where. Sometimes, there are additional conditions to be met — do you remember the second problem in the previous post?

The examples I compiled for you are simply asking to add one piece. The first two are not difficult, right? Of course, it's always an aid when one or even both kings are in check. This is similar to the colouring problems. Didn't I also write about them?

  1Andrej Frolkin  
PDB Website 03/2011
  Add one piece!(2+1)  

  2Andrej Frolkin  
PDB Website 03/2011
  Add one piece!(3+2)  

In diagram 1, the white king is missing and the illegal double check can only be avoided if we add a wKg6. Similarly, in diagram 2, we need a piece on g3. This can only be a white rook, so that the check of the wBa1 is legal. The last move was Rc3xg3+, but we can't say what was captured. This was fairly easy. But I have more to show.

  3A. Jarosch  
Schachmatnaja komposizija 79,
  Add one piece!(2+9)  

  4A. Jarosch  
Die Schwalbe 04/2007
Add one piece and resolve the position! (8+8)

Looking at the third problem, we see that the black pawns captured all missing white men, so we have to add a black piece. Obviously, this has to be on a2. We can't put a queen or a rook there, that would give an illegal check. The bishop from c8 never left this square and all black pawns are on the board. This leads to the conclusion that we have to add a black knight on a2.
Next one. In no. 4, we immediately see that the last move was b2xc1=N+, but we do not know (yet) what was captured. The bishop on b1 is a promoted piece. The black pawns captured seven times, as one came from g7. In order to accomplish this, the white pawns on d3, d4, e4 and e5 had to come from e2 to h2 and thus captured all missing eight black pieces. So, we know we have to add a white piece. The white pawn from b2 was captured right there by the black pawn that promoted into the bishop b1. After that there was only the last capture on c1. So, only the white bishop could be captured on c1. From this, we see that the white rook a1 never could leave, either wBc1 or bBb1 blocked it.
In short: Add wRa1. Last move was b2xLc1=S+. Before, the moves b3-b2 (this is the pawn from b7), b2-b1=B and bPc3xwPb2 were played (exactly in that order, but maybe with intermediate moves).

This fourth one was already a little bit tricky, but not too difficult. In the last one, no king is in check.

  5Alain Brobecker  
Jubilé TLG-50 2010
1st Commendation
  Add one piece!(8+8)  

The white pawns in diagram 5 captured eight times, so the piece to add has to be white. One of the taken pieces was the promoted black c-pawn which in turn captured once to get to the d-file. The black pawns on the board already captured six times. Hence, only the white a-pawn can be added. It never left his file, as there are no black pieces left that he could have captured. Likewise, the black a-pawn went straight to a5. Therefore, the white pawn stands on a4 (not a3 due to an illegal check).

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