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How about kf4?
The only defense to ne3 mate is qc5,
then ne3 kd4 nc2 kd5 nb4 kd4 qf6! qe5 q:e5 mate.
“The only defense to ne3 mate is qc5”
Incorrect. The following moves also work:
1. … Qb8
1. … Qc7
1. … Qf5+
1. … Qg4+
1. … Qh3
1. … Qe8
I agree that Kf4 is the winning move, though.
1. Nf4+ Ke5 (forced)
2. Qd4+ Ke6 (forced)
But then?
It looks like 1. Kf4 would be the winning move. But what about
1. Kf4 Qc6 and now I guess
2. Ne3+ Ke6
and now . . . ? Sure, White can win the pawn at c4, but is that enough?
1. Nf4+ Ke5 (forced)
2. Ng6+ fxg6 (Kd5 or Kf5 loses the Queen)
3. Qd4+ Kf5 (forced)
4. Qf4+ Ke6 (forced)
5. Qg4+ and the black Queen is lost.
5 Qg4 line is the clean solution