, , , , , , n n nA,h, , cH, z N n ,H, n ,H, B nH , , ,F, , ,GC ,
The first thing to notice is that Black is very short of moves. Only the g7-pawn can move at all. If White could pass, there would be an easy answer since 1...g6 allows a neat double-check and mate with 2.Bd2! Kd4 3.Bc3! White's difficulty is that any opening move disturbs that pattern.
Not only does one look in vain for a way to preserve the mating configuration, but the second stage of frustration is usually to look for a similar mating pattern elsewhere.
It is easy to convince oneself that the composer's intention must be something on the lines of 1.Rd8 g6 2.Kd7 Kd4 3.Kxe6 mate. Only it's not mate. Black's king sidles off to c5 and the solver goes back to the start.
The next useless idea comes on seeing that Nxh4 threatens Ng6 mate. But what can White do after 1...Kf4? Nothing in the time allotted, unfortunately.
The solver should soon be reduced to the basic template: 1.something g6 2.something Kd4 3.mate. All we have to do is find the somethings that allow a mate at move three. So put the black pawn on g6 and king on d4, and find three white moves to give mate.
Easy, Rc1, e5 and Rc4. Only the pieces don't fit together. You get as far as 1.Rc1 g6 and then can't play e5. The true answer is beautifully hidden. 1.Ra1! and now: 1...Kd4 2.e5! g6 3.Rd1 or 1...g6 2.Ra4!! Kd4 3.Bc3 mate. It's almost the same as the set mate, but the pinned b-pawn and 90-degree reflection make it very hard to spot.