- brief survey
- check every square around the King
- search for all checks
- guess why each black piece is on the board
We may miss something even after such thorough observation. But we will find them when we go through idea-verification process.
For this problem, as we noticed, white has very weak control around the black King. So there is only few ideas we can try. More than half of the 8 squares around the King are singularly guarded. We can not afford to release any of them. Among all checks, the most reasonable checkmate threat is Qf4, but that means we need help for c5 square. The only help we can get is Rc6. This naturally becomes our candidate move.
Now we enter the verification process.
First, if black does nothing, such as Bf7, can we checkmate? Yes, Qf4#. If the answer is no, our idea is wrong and we can stop there.
Second, we go through all possible defenses.
Be5 blocks our Queen, Qxa7# (Bishop also block his own Queen on h5)
Qe5 blocks our Queen, Nf3# (black Queen needs to defend f3)
Qd5 trys to block on e4, Nxe2# (black piece helps block the d5 square, and Queens needs to protect e2)
Bd5 trys to block on e4, Nxb5# (black piece helps block the d5 square and block black Queen)
Qf5 is dummy, Nxf5#
Qg5 controls f4 square, Nf3# (black Queen needs to defend f3)
Qg4 controls f4 square, Qxg7# (black Queen can no longer block on e5)
Qf3 is dummy, Nxf3#
Rf2 controls f4 square, xe3# (Rook needs protect e3 pawn)
xd2 lets Rook block on e4, Rd3# (our idle Rook swings into action!)
Why we have white pawn on g6? to prevent black Queen from going to f7 to defend f-file.
Why black pawn on h6? no Bh6.
I still don't know why we need black pawn on g2!
If there are more ideas, then we have to go through this idea-verification process multiple times. That will increase the difficulty even more.