1. Rf7, threatening 2. Rg7+ Kh8 3. Nf7# does the trick. If black plays Ne6 to prevent the mate then g6 is not defended anymore and white mates with: 1. … Ne6 2. Nh6+ Kh8 3. Ng6#
After looking at this for about 15 minutes, I finally convinced myself that white must immediately trap the king on the 8th rank, the rest then falls into place:
1. Rf7!
White is threatening Rg7+ followed by Nf7#. There is no way to cover the g7 square successfully since Ne6 is met by 2.Nh6+ followed by Ng6#. Also, black can evade being checked with Rg7 by playing Kh8, but white just follows with Rg7 anyway in a transposition. So, black is left with trying to draw by repetition, but the white king can easily evade the rook:
Incredibly the 2 knights and rook form a mating net starting with Rf7. Otherwise black’s a pawn queens.
Rf7 Ne6 Nh6+ Kh8 Ng6#
Rf7 Nd7 Rg7+ Kh8 Nf7#
Rf7 Nd7 Rg7+ Kf8 Nxd7+ Ke8 Nxc5 bxc5 Rg8+ Kd7 Ra8 Ra2 Kc1 +/-
Rf7 Nd7 Rg7+ Kf8 Nxd7+ Ke8 Nxc5 a3
Rg8+ Kd7 Ra8 a2 Nb3! Rb2 Nd4 +/-
Rf7 Ng6 Rg7+ Kh8 Nf7#
Rf7 Ng6 Rg7+ Kf8 Rxg6 a3 Nd7+ Kf7 Rg7+ Ke8 Nxc5 a2 Nb3 Rb2 Rg8+ Kd7 Ra8 +/-
Rf7 Ng6 Rg7+ Kf8 Rxg6 a3 Nd7+ Kf7 Rg7+ Ke6 Nxc5+ bxc5 Ra6 +/-
Rf7 Ng6 Rg7+ Kf8 Rxg6 a3 Nd7+ Kf7 Rg7+ Ke6 Nxc5+ Kf6 Nb3 Rb2 Rg8 Rxb3 Ra8 +/-
Ugh I did a terrible job with that analysis (I only looked at the board!) but at least I managed to find the right first move.
1. Rf7! Rg1+
2. Ke2
White threats Rg7+ Kh8 Nf7# (after e.g. a3), and more checking doesn’t help black, and I see 2 lines:
A.
2. … Ne6 (to prevent Rg7)
3. Nh6+ Kh8
4. Ng6#
B.
2. … Kh8
3. Rg7! (works fine even without check, traps king in the corner and makes f7 free) Rg2+
4. Kf1 Rf2+
5. Kxf2 any
6. Nf7#
The move Rf7 should almost play it self I guess.
1. Rf7, threatening 2. Rg7+ Kh8 3. Nf7# does the trick.
If black plays Ne6 to prevent the mate then g6 is not defended anymore and white mates with:
1. … Ne6 2. Nh6+ Kh8 3. Ng6#
After looking at this for about 15 minutes, I finally convinced myself that white must immediately trap the king on the 8th rank, the rest then falls into place:
1. Rf7!
White is threatening Rg7+ followed by Nf7#. There is no way to cover the g7 square successfully since Ne6 is met by 2.Nh6+ followed by Ng6#. Also, black can evade being checked with Rg7 by playing Kh8, but white just follows with Rg7 anyway in a transposition. So, black is left with trying to draw by repetition, but the white king can easily evade the rook:
1. …..Kh8 (Ne6 2.Nh6 Kh8 3.Ng6#)
2. Rg7 Rg1
3. Ke2 Rg2
4. Kd3 Rd2
5. Kd2 Be3
6. Ke2 any move
7. Nf7#
1. Rf7 Ne6
2. Nh6+ Kh8
3. Ng6++
I can see that I went wrong with Kf1 Rf2+ Kxf2??
Instead of Kf1? Kd3! should be played.
Seems to be mate in 7 then.
To Lorfa:
Rf7 Ne6 Nh6+ Kh8 Ng6#
Rf7 Nd7 Nh6+! Kh8 Ng6#
Rf7 Ng6 Nh6+! Kh8 Nxg6#
Rf7 Nh7 Nh6+! Kh8 Ng6#
Why change a good plan when you don’t need to change it?