Intuition quickly suggests Ng6, but it’s hard to find a proper continuation for each of black’s potential replies. I can see, for instance, that Kf7 loses in short order after:
2- Nh8+ (not a move that readily comes to mind); 2- … ; Rxh8 3- Qe6+; Kg6 4- Rg3+; Kh6 (or Kh5) 5- Qh3#
It’s even more obvious that 1… Qf7 fails to:
2- Rxe8+; Qxe8 3- Qd4+; Qf7 4- Qd8+ with mate next move
But black’s most stubborn defense must be Ra8 (or Rb8, I perceive no real difference between the two), and after that move I’m just stumped.
Looks good. Now Re8 hangs, and Rxe3 is impossible due to Qf8#. Likewise impossible is hxg6 Rxe8 Kf7 Re7+ gaining queen. First looking for defences with some counterplay (white backrank is weak):
A) 1. … Qc8? 2. Qd5+ Re6 3. Qxe6+ Qxe6 4. Rxe6 is up with rook.
B) 1. … Rc8?? 2. Qe6+ Qf7 3. Qxc8+ mates next.
C) 1. … Qc6? 2. Qxc6 Rxc6 3. Rxe8+ Kf7 4. Ra8 hxg6 5. Rxa7 was also bad.
This leaves us with things like:
D) 1. … Re5? 2. Qd8+ Kf7 3. Nxe5+ fxe5 4. Rxe5 is absolutely hopeless due to whites many threats.
E) This looks critical: 1. … Rb8/Ra8 and I have not figured it all out yet, but something in this line looks likely….
I can’t really see that this puzzle is solved yet.
E.g. after Ng6, then eiter Ra8 or Qa8 are only possibilities, but those moves look good too. Rb8? not possible. 1. Ng6 Rb8?? 2. Re7! Qc6 (Qc8/Qa8?? Qe6#) 3. Qxb8 etc. Please note that Qf7 is blacks only way to meet Qe6+, but Qf7 is also pretty efficiant.
1. Ng6 Ra8 (Qa8 also seems good) 2. Re7? Qc6 Qc6 is a very efficiant black move, threating Qc1#, you know.
The idea Nd7 is likely to be met with Qa8. Then e.g. Rxe8 Qxe8 is an impossible idea due to the Qe1# threat, and Nxf6 gxf6 Rxe3 fxe3 also looks strange.
Another idea that I have not looked into yet, is: 1. b4 enforcing the exchange of knights, but it is not immediately promising…
1. Ng6 Qc8
2. Qd5+ wins
1. Ng6 Rc8
2. Ne7+ Kh8
3. N:c8
1. Ng6 Rb8
2. Re7 Qa8
3. Qe6#
Intuition quickly suggests Ng6, but it’s hard to find a proper continuation for each of black’s potential replies. I can see, for instance, that Kf7 loses in short order after:
2- Nh8+ (not a move that readily comes to mind);
2- … ; Rxh8
3- Qe6+; Kg6
4- Rg3+; Kh6 (or Kh5)
5- Qh3#
It’s even more obvious that 1… Qf7 fails to:
2- Rxe8+; Qxe8
3- Qd4+; Qf7
4- Qd8+ with mate next move
But black’s most stubborn defense must be Ra8 (or Rb8, I perceive no real difference between the two), and after that move I’m just stumped.
Only partial credit for me, I guess.
1. Nd7 with threat of mate on Qf8 if Black captures rook
1. Ng6!! hxg6
2. Rxe8+ Kh7 (If Kf7?? Rf8 mates)
3. Qd3 and checkmate soon 1-0
1. Ng6!! Rxe3??
2. Qf8+ checkmate 1-0
1. Ng6!! Qc8?
2. Rxe8+ Qxe8
3. Qd5+ Qf7
4. Qd8+ Qf8
5. Qxf8 checkmate 1-0
1. Ng6!! Rb8 (best move probably)
2. Re7! hxg6
3. Rxb7 Rxb7
4. b4! and knight falls 1-0
1. Ng6!! hxg6
2. Rxe8+ Kh7 (If Kf7?? Rf8 mates)
3. Qd3 and checkmate soon 1-0
1. Ng6!! Rxe3??
2. Qf8+ checkmate 1-0
1. Ng6!! Qc8?
2. Rxe8+ Qxe8
3. Qd5+ Qf7
4. Qd8+ Qf8
5. Qxf8 checkmate 1-0
1. Ng6!! Rb8 (best move probably)
2. Re7! hxg6
3. Rxb7 Rxb7
4. b4! and knight falls 1-0
Nd7
1. Ng6
Looks good. Now Re8 hangs, and Rxe3 is impossible due to Qf8#. Likewise impossible is hxg6 Rxe8 Kf7 Re7+ gaining queen.
First looking for defences with some counterplay (white backrank is weak):
A)
1. … Qc8?
2. Qd5+ Re6
3. Qxe6+ Qxe6
4. Rxe6 is up with rook.
B)
1. … Rc8??
2. Qe6+ Qf7
3. Qxc8+ mates next.
C)
1. … Qc6?
2. Qxc6 Rxc6
3. Rxe8+ Kf7
4. Ra8 hxg6
5. Rxa7 was also bad.
This leaves us with things like:
D)
1. … Re5?
2. Qd8+ Kf7
3. Nxe5+ fxe5
4. Rxe5 is absolutely hopeless due to whites many threats.
E)
This looks critical:
1. … Rb8/Ra8
and I have not figured it all out yet, but something in this line looks likely….
1. Nd7, Rd8
2. Qe6+, Kh8
3. Qe8+, Rxe8
4. Qxe8#
I can’t really see that this puzzle is solved yet.
E.g. after Ng6, then eiter Ra8 or Qa8 are only possibilities, but those moves look good too. Rb8? not possible.
1. Ng6 Rb8??
2. Re7! Qc6 (Qc8/Qa8?? Qe6#)
3. Qxb8 etc.
Please note that Qf7 is blacks only way to meet Qe6+, but Qf7 is also pretty efficiant.
1. Ng6 Ra8 (Qa8 also seems good)
2. Re7? Qc6
Qc6 is a very efficiant black move, threating Qc1#, you know.
The idea Nd7 is likely to be met with Qa8. Then e.g. Rxe8 Qxe8 is an impossible idea due to the Qe1# threat, and Nxf6 gxf6 Rxe3 fxe3 also looks strange.
Another idea that I have not looked into yet, is:
1. b4
enforcing the exchange of knights, but it is not immediately promising…
1 Ng6 Qa8
2 Rxe8+ Qxe8
3 Qd5+ Qf7
4 Qd8+ (mate next)
1 Ng6 Ra8
2 Re7 Qc8
3 Qd5+ (mate next)
pft is right about
1. Ng6 Ra8
2. Re7? Qc6!
I tried
1. Ng6 Ra8
2. Qe6+ Qf7
3. Ne7+ Kf8
4. Qd6 (threatening Nc8) but
… Nc4
so I’m stumped too.