A. Klibanski and N. Plaksin
2nd Prize feenschach 1977
13+10. (Grid-Chess) (a)
Where have the missing men been captured?
(b) First move of the Black King?
Solution: wKB was captured at home. The wK could only reach g1 through O-O. Black did just play Qb1xd1+.
The wR now on a2 could only reach a2 from higher up on the a-file. Which requires cross-captures a2xb3 and b2xa3, in that order. Thus the sequence has been (1) wNb3-a1, (2) then wPa2xb3, (3) then wRa-a2, (4) then wPb2xa3, (5) then wBc1-b2. The actual wRa2 must be a promotee (can't be wKR after O-O) and the original wRa1 has been captured on its home square. Then the wKR has just been taken on d1.
The promoted R requires the sequence wPh2-h4xg5xf6xe7xd8=R. This (and the a-b cross-captures) account for all missing black units, so that the bPe7 is part of these captures, and has been taken on e7, forcing the g5 and f6 captures to be bl. Knights. The bQB is white-squared and has been taken on b3.
The bK was not on e8 when e7xd8=R occurred. He could only have escaped e8 with O-O-O (hence his first move !) because square e7 and bBf8 had never been free before. So that the bQR was taken on d8 and the bKR on a3.