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1) Nf6+; Kh8 – 2) Ne8 …..anything else?
Black would not have to capture the Knight on e8. Instead, Black could move f6, allowing the Queen to defend against mate on g7.
But 2.f6 results in 3.Qf8#
1.Nf6+ Kh8
2.Ne8 Qc5+
(2….. Qe5 3.Qf8#)
3.Kh1 Qg1+
4.Kxg1 Rxe8
(4…. c1=Q 5.Qg7#)
5.Rxe8#
if 3.Kh1 then black rook takes knight at e8, followed by 4. rxr + q f8 interposes
5. wgite can mate in 3 manners: by q g7 or the rook or queen captures the black queen
[earlier, if check at c5 with queen, it is illustrative to see that k to h1 is significantly better than h2 or f1]
Though Black’s queen is left hanging by moving f6. I worked out:
1. Nf6+ Kh8
2. Bxc2 Bxc2
3. Re8+ Rxe8
4. Nxe8 Qc5+
5. Kh1 Qe5
6. Qf8#
1. Nf6+ Kh8
2. Bxc2 Qxc2
3. Re8+ Rxe8
4. Nxe8 Qc3
5. Qf8#
I see mate in four. 1).Nf6+; Kh8 2). Re8! ; Rxe8 3).Nxe8!; f6 4). Qf8++
although in your scenario 3. knight takes rook at e8 threatens both mate and the black queen, black can escape with 4. q c5 + or by promoting the pawn…
I see mate in four. 1).Nf6+; Kh8 2). Re8! ; Rxe8 3).Nxe8!; f6 4). Qf8#