With Black's king firmly nailed to h6, all White needs is a check and it's mate. His knight on e6, however, cannot move without letting the king escape to g7. The obvious idea is 1. Ng3, but when the threat of Nf5 mate is met by 1 . . . Ne7 there is nothing for White to do next. With the bishop free to wander along the diagonal, nothing can tempt the knight to move away from e7.
However, suppose it is Black's move in the diagram position. 1 . . . Ne7 would lose to 2. Nxf6 when the knight must move allowing Ng8 mate; any bishop move on the long diagonal would allow 2. N4xg5 and 3. Nf7 mate; and 1 . . . Be7 would take away the knight's essential defensive square, thus allowing 2. Ng3 and 3. Nf5 mate.
So if White can find a decent passing move, Black will have no choice but to play 1 . . . Bd8. And when you put Bd8 together with Ne7., you arrive at a severe traffic jam. We now have the basis of a solution: 1. (pass) Bd8 2. Ng3 Ne7 3. (pass) N anywhere 4. Nf5 mate. All you need is to find the right king moves to fill in the passes.
You may now either guess the answer, or get there by a process of elimination. 1. Kc8? loses too much time by allowing Ne7+; 1. Kxc7? allows (among other things) Be5+; 1. Kxa7 moves within range of a bishop check on d4 (or even Ne7 and Nxc6+); 1. Kb8 allows 1 . . . Ne7 2. Nxf6 Nxc6+ 3. Kxc7 Ne7 - again there is no mate on the fourth move.
So the answer has to be 1. Ka8] Bd8 (as explained above Be7 is met by Ng3, other bishop moves are met by N4xg5, and Ne7 is dealt with by Nxf6) 2. Ng3 Ne7 (to defend the threatened mate on f5) 3. Kb7]] Now the knight must move and cannot give a check. So White mates, on schedule, with 4. Nf5.
This elegant composition won a first prize for its composer, Gabriel Leon Martin, when first published in 1932.
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