If it were Black to play, he would be dead: his only move is 1 . . . g3, when 2. fxg3 f2 3. Nc2+] bxc2 4. Nxf2 Ka2 5. Kxc2 lets the g-pawn queen and deliver mate on a8. The trouble is that White cannot easily lose a move. Since 1. Kd2 Kb1 2. Ke1 Kc1 is worse than useless, he must try to do something with the knight on b4.
The idea that should suggest itself is to use the knight to free the king. If White's knight can get to a3, guarding the b1-square, then the king can move away. So the plan takes shape: manoeuvre the knight to a3; take the king to g1, and play Kh2, Kh1 and Kg1 to lose a move; return the king to c1 and the knight to b4. All of which should reach the diagram position with Black to play.
Okay, let's see if it works: While Black's king oscillates between a1 and a2, White plays 1. Na6, 2. Nb8, 3. Nd7, 4. Nf6, 5. Nh5, 6. Ng3, 7. Nf1, 8. Nd2, 9. Nb1 and 10. Na3, then 11-21. Kd2-e1-f1-g1-h2-h1-g1-f1-e1- d2-c1. Moves 22-31 retrace the knight's moves 1-10 in reverse order, ending with 30 . . . Ka1 31. Nb4. Black must now play 31 . . . g3, when the end is reached with 32. fxg3 f2 33. Nc2+ bxc2 34. Nxf2 Ka2 35. Kxc2 Ka1; the g-pawn queens on move 40 to give mate on a8 on schedule at move 41. Bravo]Reuse content