Daily chess puzzle: Check Mate #243
Another puzzle from Dragoslav Andric’s 1981 book “Matni Udar”.
White to play and mate Black

Muller v unknown, 1961
Solution
You know the score: how to land a blow on g8 or f7?
The obvious moves fail, but when you see 1 Qf7!!, it is immediately clear it is game over: though Black has many defences, and each need to be worked through.

The non obvious point is “what does Qf7 threaten”? The reason I saw it was that the Rf8 is tied to the 8th rank (g8), but Q*f8 isn’t protected. The move 1 Qf7 actually threatens 2 Qd7, the Rd7 being LPDO; whilst also threatening the much more severe 2 Rg8+ or 2Qg8+.
So, the main point is 1…Rdf7 2 Rg8! Rg8[] 3 Nf7 mate.

Black’s other main try is 1…Qg3 when simply 2 Qd7, taking the LPDO, is 1-0: Black’s Bb7 is also LPDO and falls, since Black’s Queen must defend g7.
This puzzle is a good example of the importance of LPDOs: had the Bb7 been protected, the combination wouldn’t work.
FEN
5r1k/pb1r3n/1p5N/2p1qN1Q/4p3/1P4R1/1P4P1/5RK1 w – – 0 1