White to move and checkmate in 4 
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This one is tough!
hmm all I could come up with without moving the pieces is:
Nfg5 kg8
nf6+ kh8
Ne6 Re5+
Kf3 Re3+
Kxe3 h3
Rg8++
Nfg5 kh8
nf6 h3
Ne6
which is not mate in 4.
1.Nfg5+ Kf8 [1…Kg8 (1…Kh6 Rh7#)2.Nf6+ Kh8 (2…Kf8 3.Ne6#) 3.Nf7#]2.Ne6+ Kg8 [2…Ke8 3.Nf6#] 3.Nf6+ Kh8 4.Rb8#
addendum: 1…Kh8 2.Nf6 with Nf7# to follow. If 2…Rh7 to prevent 3.Nf7# then 3.Rb8# If 2…Rg5 3.Rh7#
Oh I think instead of spite checks like Re5+ (which increases the move count) black plays Rb5 instead of Re5+ and then white plays Rh7++.
1. Ne5+ Kf8
2. Rf7+ Ke8
3. Nd6+ Kd8
4. Nc6#
hi chesstraveler,
sorry, but after 2. …Kh8, 3. Nf7 is not mate because of 3. …Kg7, right?
Otherwise, always baffled by your solutions… 🙂
Bernd
I too thought it was tough at first because I kept doubting my solution & asking myself if 1.Nfg5 might be the correct move after all. But those were just delusions. The first line I thought of was the correct one:
1.Ne5+ Kh6, 2.Ng4# or 1.Ne5+ Kh8, 2.Nxg6+ Kg8, 3.Nf6# or 1.Ne5+ Kg8, 2.Nf6+ Kh8 or Kf8, 3.Nxg6# or 1.Ne5+ Kf8, 2.Rf7+ Kg8, 3.Nf6+ Kh8, 4.Nxg6# or 1.Ne5+ Kf8, 2.Rf7+ Ke8, 3.Nd6+ Kd8, 4.Rd7#
Take very good care all & have a great day. Cheers!
Bernd, You’re right. Trying to solve these right before going to bed at night might not be the best plan. Anyway, upon further review, 2.Ne6 Re5+ 3.Kf4 Re6 4.Rh7#.
Hi Susan
1. Ne5, Kf8 [1. …, Kh6 2. Ng4# Mate; if 1. …, Kg8 2. Nf6, Kf8(2. …, Kh8 3. Nxg6# Mate)3. Nxg6# Mate; 1. …, Kh8 2. Nxg6, Kg8 3. Nf6# Mate]
2. Rf7, Ke8 (2. …, Kg8 3. Nf6, Kh8 4. Nxg6# Mate)
3. Nd6, Kd8
4. Nxc6# Mate
Good day
Hi chesstraveler,
great, thanks for the clarification, and have a good night… 🙂
Bernd