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1. … Ng4 2. fxg4 Ne3 3. Rxf8+ Rxf8 4. Nxe3 (4. Rf2 Rxf2 5. Nxe3 [5.Bxf2 Qxg2#] Qxh2#) Rf1+ 5. Nxf1 Qxf1#
1…. Ng4 threatens Q:h2#, and 2. Bg3 is not an option due to …N:g3+ and mate next. Whiten is therefore forced to play
2. fg Ne3 threatens Q:g2# (among other things)
3. R:f8+ R:f8 white buys time
4. N:e3 Rf1+
5. N:f1 Q:f1#
It just sort of plays itself once you see 1….Ng4.
It all starts with Ng4! Threatening mate on h2. So, forced: fxg4, now Ne3, threatening mate on g2. The open f-line could give white an extra move, but since black recaptures with a rook and the white Bishop is blocking the white second rook, it only makes things worse. No matter what white does, with the f-file open it will only take 3 more moves to mate.
Cute Key line
Ng4 g4
Ne3 Rg1
Nf1 Bg3
Ng3
Marvellous puzzle!
Opening f file seems to be a theme:
1. Ng4! fxg4 (only against Qxh2#)
2. Ne3!
Double threat Qxg2# and Rxf1# (Nxc2 is of less interest here).
Decisive is that white never gets tempo to move his Be1 to get help from Rc1!
Or play e pawn to get help from Q.
A)
2. … Rxf8+ (Nxe3 Rxf1+ is 1 move shorter)
3. Rxf8 (double threat remains) Nxe3 (only against both)
4. Rf1+ Nxf1
5. Qxf1#
B)
2. … Rg1
3. Ng4! any
4. Qxh2#
C)
2. … Rf2
3. Rxf2! Nxe3 (Bxf2 Qxg2#)
4. Qxh2#
Ng4 followed by Ne3
we might want to clear the f-file to bring in our rooks against the disconnected white ones. Nf6-g4 as well as Nf5-e3 and Nf5-h4 could help clear the file with tempo threatening mate on h7/g7. Nf5-h4 can be dismissed, because Be1xh4 would solve all white’s problems stopping mate and connecting rooks. Nf6-g4 only forces fxg4 if the remaining knight is still on f5 hitting g3. So the clearance would follow the move order 1… Nf6-g4 2.fxg4 Nf5-e3 double mate threat, 3.Rxf8 Rxf8 still double mate threat 4.Nxe3 Rf1+ 5.Nxf1 Qxf1#