Solution

White to play and mate in eighteen. The composition is also sound as a study.

1.Bd5+ Kg1
2.Bc5+ Kf1
3.Nd2+ Ke1
4.Nf3+ Kd1!

4...Kf1? 5.Nxh2+ Ke1 6.Nf3+ Kf1 7.Kxg7+-. Leads to a quicker mate..

5.Bb3+ Kc1
6.Ba3+ Kb1
7.Nd2+ Ka1

White has played three switchbacks. The black king has had a forced march along the eighth rank.

8.Bc2

Threatening mate and thus forcing Black's hand.

8... Rxh7+
9.Kg8 Rh8+
10.Kf7

10.Kg7 Rh7+ 11.Kg8 (11.Kf8 Be7+) 11...Rh8+ 12.Kf7 Rh7+ transposes.

10... Rh7+
11.Ke8

11.Kg6? Rh6+.

11... Rh8+
12.Kd7 Rh7+
13.Kxd8 Rh8+
14.Kc7

14.Kd7 Rh7+ takes one move longer.

14... Rh7+
15.Kb8! Rh8+
16.Kxa7 Ra8+
17.Kxa8

White's king also completes a corner to corner trip!

17... e1Q
18.Nb3 Checkmate.