I analysed one, but the simulation did not allow me. 1. Kb8 (or Ka6) Nc3 (or Nb3, or Nd2) 2. Rd2# CHECKMATE Resolution : 1. The black king is blocket. 2.If you move the white king, the black rook get blocked too (for the bishop checks king otherwise). 3. wherever black knight goes, he can't avoid mate in Rd2. The other solutions proposed by the puzzle are nice too.
The one flaw in your analysis is that you've ignored the fact that the knight doesn't have to move. There are two black pawns in this position for a reason, and while e4 also leads to mate in 2 (Qd7#), f5, simultaneously threatening the queen, blocking its access to the d7 square, and opening up an escape square on e6 for the king, doesn't. After 1.. f5, there's no piece that can deliver checkmate on the next move. That's why your solution wasn't accepted as an alternative.
I immediately rejected any King move, because there would be two solutions (dual) which is not allowed in compositions. What helps me to solve this kind of problem is to find out which checkmates White has available if Black plays first. Then find the move that makes the missing checkmates possible.
It was the presence of the f6 pawn that led me to the solution. The start position is almost a zugzwang - if only there were a way for white to mate on e5 after the f6 pawn moves. The queen seemed the likely candidate for mating on e5, but after eliminating all possible queen first moves I tried the rook.
1. Kb8 (or Ka6) Nc3 (or Nb3, or Nd2)
2. Rd2# CHECKMATE
Resolution : 1. The black king is blocket. 2.If you move the white king, the black rook get blocked too (for the bishop checks king otherwise). 3. wherever black knight goes, he can't avoid mate in Rd2. The other solutions proposed by the puzzle are nice too.