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1. Rg3! Qe7 2. Rg8!+- winning the queen. If 1. … Qe1+ 2. Kh2 and there is no way to avoid the checkmate.
Wow, this is a nice one: 1.Rg8+! Rxg8 2.Qc3+ Rg7 3.Qc8+ and wins. Black appeared to have everything covered but not quite.
Beelze
It doesn’t work.
I think
R-g8+ Rxg8
Q-c3+ Q-e5
Qxe5+ R-g7
Q-e8
I was looking at
1. Rg8+ RxR
2. Qc3+ Rg7
3. Qc8+ Rg8
4. QxR ++
I see a mate in 5, unless I am really, really brain dead today..
1. Rg8 Rg8
2. Qc3 Rg7
3. Qc8 Qe8
4. Qe8 Rg8
5. Qg8#
Rg8 – Rxg8
Qc3 – Rg7
Qc8 ???
1. Rg8+ Rxg8
2. Qc3+ Rg7
3. Qc8+ Rg8
4. Qxg8#
I think Morsa´s line doesn´t work because after 1. Rg3 black can play 1. … Qd4, defending the checkmate and threatening Re1+.
The winning move is Morsa´s number two, but it must be played immediately:
1. Rg8+!! Rxg8
2. Qc3+!
and now white either checkmates
2. … Rg7
3. Qc8+ Qe8
4.Qxe8+ Rg8
5. Qxg8++
or wins black´s queen and bishop, after black´s best defensive move:
2. … Qd4
3. Qxd4+ Rg7
4. Qxd3 (+-)
1. Rg8+! RxR
2. Qc3+ Rg7
3. Qc8+ Rg8
4. QxR++
1. Rg8+ Rxg8 2. Qc3+ Rg7 3. Qc8+ Rg8 4. Qxg8#
Qc3
1.Rg8+! Rxg8 (forced)
2.Qc3+ Rg7
3.Qc8+ Rg8
4.Qxg8#
1. Rg8+,R*R
2. Qc3#
1. Rg8+ Rxg8
2. Qc3+ (very mean) Rg7
3. Qc8+
and finito
1. Rg8+ Rxg8
2. Qc3+ Rg7
3. Qc8+ Rg8
4. Qxg8#
1.Rg8+ Rxg8 2.Qc3+ followed by mate.
1 Rg8+ Rxg8 2 Qc3+
x. Qc3
X. Qc3
I would try Rg8+ Rxg8 Qc3+ Rg7 Qc8+..
Qc3 looks good, threatening mate and protecting e5.
1. Rg8+ Rxg8 2. Qc3+ Rg7 3. Qc8+ and mate coming.
1. Rg8+ Rxg8
2. Qc3+ Rg7
3. Qc8+ 1-0
As Ivan pointed out, only 1. Rg8+ forces a response. 2. Qc3+ does not force a single response. Black can opt for a slower death by 2. … Qd4