5bQ1/6p1/p5K1/P3p3/1P1pkp2/3p1p2/3P1P2/8 w - - 0 1
You do enough of these, you start to recognize certain things quickly- in this particular puzzle, I noted within about 5 seconds that black had only one man that could move as long as the queen stayed on the a2/g8 diagonal. After noticing that, I immediately realized that all white had to do was to find a square on that diagonal from which he could place the queen on a rank or file next to the bishop on the next move- which black would have to move from blocking the mate on the a8/h1 diagonal. For one of the few times, I found a mate in 3 easily.
It took me 15 minutes to solve this puzzle.
1, Qf7? Be7!
- Qe6? Bd6!
- Qc4? Bc5!
- Qb3? Bxb4!
- Qa2! 1... Be7/Bd6/Bc5/Bxb4 2. Qf7!/Qe6!/Qc4!/Qb3! and checkmates on the a8-h1 diagonal.