Mate in 2, composed by George Koltanowski

https://lichess.org/study/0HPQGJ1Y/sSgUx8Dm

The first question I ask myself is this:

What would happen if it were Black to play?

Both 1...Kh3 and 1...Kf2 are met by 2.Qe5-g3 mate.

But White currently has no answer to 1...Kh1 or 1...Kg1.
We must either prevent those moves altogether, or make sure that there is an immediate mate there.

We could try 1.Qe1, to prevent them. That comes close! Then 1...Kh3 2.Qg3 is mate.
Unfortunately, there is no mate available after 1.Qe1 Kh2!

What about bringing the knight from d2 to f1 or f3? That would allow a mate with Qe5-h2. The fact that the knight can be taken should not dissuade us from checking this move. In composed problems, the first move often allows a capture.
In case of either knight move, there are several Black responses to consider

1. 1...Kh1
2. 1...Kh3
3. 1...Kf2
4. 1...K(x)f1
5. 1...K(x)f3

The solution is 1.Nf3!

The mate after 1.Nf3 Kxf3 2.Qe2# is an unusual form of the 'Dovetail mate'.