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[2]
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Black lives only if White plays this sequence follishly to allowing Blace to capture at a. White can play b as , , , or even to connect to White's two stones and thus kill the main Black group even if allowing Black's few stones on left to escape if they can. The longer White delays in playing b after , the better for Black.
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If White comes from the inside with , she can't capture because of the snapback. The successive throw-in of qnd are the tesuji here.
If White comes from the other side, forces to capture, then connects at . This is more straightforward than the main line.
Likewise exchanging - doesn't change the solution. connects at and then we're again at either a (main line) or b (variation)