Retrograde problem 1

Note that either one of the kings are in double check at the moment, so the previous move had to be a discovered check of some sort. At first it seems impossible to get a double check from a previous position, but considering the rules of promotion helps find the last move.

Since Qc6 and Rd8 are double checking either Kc8 or Kd6, we can say they are both of the same color. From observation it is clear that Rd8 wasn't a part of the board the last move and was promoted from a pawn on either c7,d7, or e7. But if the pawn was on d7 or e7, Kc8 would be in check, which is not possible. Hence, there was a pawn on c7, and we can conclude there existed some piece on d8.

From this we can conclude that Qc6, Rd8 (Previously c7) and Kd6 are white while Kc8 is black.

Now to allow white to make the move c7xd8=R+, there should've been no other checks in the previous move. Hence Rf6 and Ne8 are white while b7 is Black. Since the board is oriented with white starting at the bottom (evident from the promotion), we can say there is no way for a bishop to land on a8 unless it was a white bishop, promoted from an a7 pawn, and hence the pawn on a7 right now should also have been white.

And finally the black piece on d8 in the previous move had to be a knight, since if it was either a rook, bishop or queen, the King on d6 could not move to this position.

Before the last move, Black had 3 pieces. A king, a pawn and a knight.

The only possible valid last move was a discovered double check.

Perhaps the reader would prefer to work out the rest of the details.

First I realize that the pawn in (1,6) should be white, otherwise the bishop cannot be in (0,7).

Then without other revealing, you can easy match the value of pieces with the possible answer and the only valid options is 12, for 2 pieces with total value 6