What can Black’s f5 bishop threaten? The two White pieces on light squares: the rook and knight, but not at the same time (the possible attacking moves are Be6, Be4, and Bxc2). Attacking the rook with Be4 has the interesting result of also attacking a square—h1—next to White’s king. In the previous problem this was exploited by forcing the enemy king onto the targeted square with a check. Here there is a different possibility. Consider the White king and the constraints on its movements. The back rank is owned by Black’s rook. If the bishop were attacking h1, Rh1 would be mate. So no setup is needed. Be4 threatens the rook and threatens Rh1#, thus winning the rook without any need to force White’s king into a more vulnerable position.

The lesson is to take notice if a bishop can attack both an enemy piece and a square next to the king. It may be that a preliminary exchange will allow you to move the king and so then check with the bishop move, or that aiming the bishop at that square will itself produce a mating threat that works just as well as a check as an anchor for the fork.