Meisterwerke

The only way to give mate in 1 is to add the wh. Rook on b1 or c3 and play 1. b3#. Now, what is the right square for the Rook ?

Counting missing White pieces: including the Rook which is to be placed, and the Wh. KB which fell on its home square (f1), there are two other missing pieces: a wR and a wN. One of these fell on f6.

Now, White's h-pawn made one capture, on a black square, to reach g3. White's c-pawn captured the remaining Bl. pieces via c2xd3xe4xf5xg6xh7, all on white squares. So White's h-pawn must have captured the Black KB, and White's c-pawn captured a bP (or its promoted replacement), two N's, a Q and a R. For the Bl. b-pawn to be captured by W's c-pawn, it would have to have made at least two captures (or else it made one capture to get to the c-file and the c pawn made one capture to get to the d-file). In either case, there is only one remaining White piece to be captured (whichever one was not captured on f6). So the Black b-pawn must have promoted and made at most one capture in doing so. It must therefore have captured a piece on a2 and promoted on a1.

So, the wN and wR were captured on a2 and f6 (though not necessarily in that order). However, Bl.'s KB could not have gotten out to be captured on g3 until after the capture on f6. As the Wh. QR was permanently confined to a1-a2-b1, neither wR could have gotten out to be captured until after the capture on f6. Thus, the wN was captured on f6, so a wR (necessarily the QR) was captured on a2. So it must be the Wh. KR that is supporting the pawn delivering mate. Since the Wh. KR cannot get to b1, it must be on c3.

Solution by Philippe Schnoebelen