...can be tedious. 16 moves for Queen's first move alone, 17 for the Bishops.

Enter logic ~ Which moves produce a position where BK has the FEWEST available squares for moving to?
• g6B: 3
• Kt: 2
• g3B: 1
• Q: 0
After 1. Qe3 and 1. Qe5, it's Stalemate, no good.
After 1. Qg1...K×g5, leaving no prospects.

Only one move guards all vulnerable pieces AND leaves BK with only 1 square to flee to: 1. Bh4.

The g3B has 3 squares to go where it's guarded: f2, h4, e5. From only one of these does it guard g5N: 1. Bh4.

With two marks in its favor, try Bh4.
1. Bh4...Kf4 (forced)
2. Qe4# (guarded by Kt)