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Black Win
Rxg1+!; Kxg1 Rag8+; Kh2 Qf4+ Kh1; Ng3+
Rxg2 seems to be winning.
if … Kxg2
Rg8+ Kh2
Qf4+ followed Ng3+
after Rg8+
Kh1 or Kf1 gets
Ng3+
1. … Rxg2+
2. Kxg2 Rg8+
3. Kh2 Qf4+
4. Kh1 Ng3+ winning the Q
1. … Rxg2+
2. Kxg2 Rg8+
3. Kh2 Qf4+
4. Kh1 Ng3+ winning the Q
…Rxg2+
Kxg2 Rg8+
kh2 Be6+
Kh1 Ng3+ (fork the K & Q)
An alternative line that has not been pointed out yet involves White interposing the doomed queen:
1. ..Rxg2+ 2. Kxg2 Rg8+ 3. Ng5 Rxg5+ 4. Qg4 Qxf2+ 5. Kh1 Rxg4 6. Rc8+ Kg7 7. Rg8+ Kxg8 8. hxg4 Ng3#