White to move. How should white proceed?
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1. Rxh5+. Qxh5.. 2. f6+.
2….. Rg6. 3. Rxh5+. Kxh5. 4. Qh4+!!
2…..Be4. 3. Bxe4+. Rg6. 4. Rxh5+. Kxh5. 5. Qh4#
2…..e4….3. Bxe4+. Bxe4. 4. Qxe4+. (Kh1. 5. Rxh5#). Rg6. 5. Rxh5+.(if Kxh5. Qh4#) Kg8.6. Qxa8#
Black can make it mate in 8 with the right moves, but K.V. has the right lines other than that- that I can see. The white pawn at f6 covers the escape square of g7 allowing Qh4# in several of the lines.
The checkmate in 8 is indeed the longest line Black can survive. 1. Rxh6+ Qxh6 2. f6+ e4 3. Bxe4+ Rg6 4. Rxh6+ Kg8
5. Rxg6+ fxg6 6. Qxg6+ Kf8 7. Qg7+ Ke8 8. Qxe7# All other variations are faster checkmates.
Nice problem, 2…e4 is the best defence but as pointed, it doesn’t quite work.