R: 1. ... 0-0 2. Ld5-a8 b7-b6, dann 1. ... Txh8+ Kd7 2. Dxc7#
One of the best tests for thoroughly understanding problems of this class is to play a game up to the position. If the solver succeeds in doing so he will find that he has made the moves which are to be retracted, as such must be made to arrive at the position.
A better way is to give the problem an analytical examination, count the numer of captures made on either side, and note where each of the men played from, when and how they played, was it by capturing or otherwise. In the above problem we note that White lost a R only, which must have been captured by Black's KP [e7xf6], as its position shows that it made a capture. Black lost six men, the number off the board. His QP at Q7 [sBd2] did not play from B6 [c3xd2?] ass it made no capture, and consequently could not have moved last, neither could his QKtP [sBb7] or KP [sBe7], otherwise White's Bs could not be where they are. His KRP [sBh7] is off the board - our analysis will presently account for how it was captured. It is obvious that his R at R3 [sTa6] could not have played last, neither could R at RBsq [sTf8], as then the White K would have been in check, and it is not allowable to suppose that it remained in check.
Now the question is, Could Black's last move have been K from Rsq to Ktsq [sKh8-g8], moving from a check given by the R? This, we find on a further analysis, could not be, as the White R did not capture Black's KRP, consequently it could not have given check at the square it stands on. None of the White's pieces made a capture, the men were taken by his Pawns only, QP at QR5 [wBd2xc3xb4xa5] took three, and KP, KBP, and KRP took one each [wBe2xd3,wBf2xe3,wBh2xg3], none of them could have taken a P, consequently it follows that six Black pieces off the board were captured. There are only five Black pieces off the board, also a P, that P is Black's KRP [sBh7], which moved down the file to R8 [h1], was promoted to a Piece, and duly captured.
After all this we find that there is only one possible move Black could have made on his last, and that was Castles, this we accordingly retract. Having retracted it, we look to see what move White could have played for his last. All his men appear to be free, that is, not confined as Black's are, and it may appear difficult to determine what his last move was. In this case we look to see what Black's second last move could have been.
He did not play K or KR [sTh8] as he was able to castle after, neither could he have played QR or QP [sTa6,sBd2], it is also obvious that he did not play KPxR [sBe7xTf6], in consequence of the B at Q8 [wLd8 (außerdem auch, weil sonst der sLf8 als Schlagobjekt fehlt)], but if the B at QR8 [wLa8] were not there he could have played P to Kt3 [sBb7-b6]; consequently to allow of this second last move of Black's, White must retract a move made with his KB. There is only one square it could have played from and that is Q5. Therefore B at Q5 to R8 [wLd5-a8] was White's last move, and P at QKt2 to Kt3 [sBb7-b6] was Black's second last move.
White for his last move could not have made a capture with any of his Ps as Kts stand behind QP and KBP, the KP played early in the game to allow KB to play out, and KRP did likewise to allow Black's RP to play to R8.
The conditions of the problem do not ask for more than two of Black's moves to be retracted, yet the solver could demonsterate what his third last move was, viz., R to R3 [sT-a6].
On word as to the line of play leading up to the position. It may be considered very bad play, and it would be such were it played as a game, burt no matter how improbable the line of play may be, as long as the moves are possible they are sufficient to prove that the position can be arrived at and consequently sound.
Having retracted the moves in the problem [1. ... 0-0 2. Ld5-a8 b7-b6] we give, White mates by 1 RxRch, I K to Q2, 2 QxBP mate.