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I think this is a mate in 4. Black is threatening Rc1# so checks are needed.
1.Ne8+ Kf8 2.Nf6+ Ke7 (3.Kg7 Rg8#) 3.Rd7+ Kf8 4.Rxf7#
1.Ne8+ other K moves 2.Nf6+ Kg7 3.Rg8#
1. Ne8+ Kf8 2. Nf6+ Ke7 3. Nc6#
or
1.Ne8+ K other 2. Nf6+ Kg7 3. Rg8#
I see the mate in 4 James offers. However, CraigB’s mate in 3 appears to cook, with 3 … Rxc6.
Black’s own threat concentrates the mind.
I’m late to my party, but the first three comments describe my thought process exactly.
1 – this seems like a mate in 4
2 – no, but I can mate with Nc6
3 – wait, what about Rxc6?
If this was a constructed puzzle, the point of the N at e5 must be for Nc6#, so perhaps there’s something missing?
*late to this party
We really need a comment edit function
Good idea: let’s put a black pawn or N on c5 and we have checkmate in 3! 🙂
@philosopher55: BRAVO! Either would suffice for a neat mate in three!