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RE: Chess problem 61 / Schachaufgabe 61
Yes, White can with 4. Rg5. The idea is to play 5.Rh5 next - if the rook is taken then the mate sequence is 6.Qg5+ Kh8/h7 7.Rh6 mate!
If Black plays 1...Bxe8 (idea: 2.Rg5 Nxe5! 3.Rh5? Ng4! check and the queen on h6 will be taken on next move) instead of 1...Qxe8 (idea: Qd8 keeps in touch with rook on f6 to enable the defence Nxe5 as shown) then 2.R5xg6 wins as the rook on f8 is unprotected now (no queen on e8!)
If this is the right solution 1.Ne8 is a wonderful move and very hard to be seen :-)
After Rg5, Nxf2 and nothing is threatened. Blacks can promote their pawn peacefully while drinking soda and there is no way to avoid it unless whites move one of the pieces threatening a checkmate, losing the game.
Good objection :-) If I play 5. h5 then? Blacks position is pretty cramped and I don't see a defence against 6.hxg6 and mate soon. In that case White will drink soda :-)
By the way: One white rook is on f6, so there is no piece taking on f2. The whole line we discuss is:
1.Ne8 Qxe8
2.Rf6 g6
3.Qxh6+ Kg8
4.Rg5 now if
a) 4...Nf2 5.h5
b) 4...Nxe5 5.Rxe5 renewing the threat Rh5