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only one move that puts the white king in check without sacrificing a queen…
too obvious
This is a repeat
Bxd4
It was not too obvious; It took some trial and error to find.
1..Rxg2+!!
2. Kxg2 Rg8+
Now there are two lines:
a) 3. Kh2 b) 3. Kf1
The first line is the nice one:
3. Kh2 Qf4+
4. Kh1 Ng3+
5. Kg2 Nxe2
6. Kg1 Nxc1 With an overwhelming material advantage plus possible mating traps.
The second line is simpler than the first:
3. Kf1 Ng3+
4. Ke1 Nxe2
5. Rxe2 Qxb3 or 5..Qxf3 and
Black has a clear winning advantage.
To wrap it up I want to add two more small lines:
On 1..Rxg2
Instead of 2. Kxg2 what happens if the King goes to h1 or f1. So
2. Kh1 Nxf2+ 3. Kxg2 Qxe2 wins for Black.
And 2. Kf1 loses to 2..Rxf2+