Black has moved his bishop back to g7, forcing the question of the White queen’s intentions. Should the queen retreat? The prospects for mate might seem remote. The bishop blocks the long diagonal to h8, the files leading to Black’s king are closed, and White has no knight able to give check. But the White bishop aimed down the long diagonal from b2 still is provocative, especially when White has his own knight on the same diagonal on d4. This formation is the kernel of a discovery and it allows White to inflict a double check—if he can get Black’s king onto g7. That result is easy enough to arrange. You just have to be open to the idea of a queen sacrifice: 1. QxB+, KxQ; 2. Nf5++, Kg8; 3. Nh6#.

The position works the same way if White’s queen starts on e5. The point still is to get the king onto g7 with a sacrifice, and then to move the d4 knight to h6 in two steps—the first of which is a double check that gives Black no option but to move his king. (Notice that there needs to be a Black pawn on g6 so that after the double check the king can’t move there. The knight itself seals off h6. You needn’t remember these particular details, but you do need to remember to account for all flight squares.)

These last two examples both have shown how a knight can spend multiple moves getting into position to mate with a bishop. The key in both cases is a clever use of discovered check, playing with ways the knight can jump on or off the long diagonal on its way to the mating square. Both positions also involve sacrifices of queens to attain the desired pattern. Once you determine that a mate is nearby using pieces other than the queen, a queen sacrifice to take out the obstacles to it should not faze you.