Is it possible for this black group to live?


I was playing a game earlier, and near the middle of the game, I managed to play two stones inside black’s territory (by peeping once and extending). At the end of the game, I analyzed this and couldn’t find any possible way for black to live. Could any higher-ranked players help me out here?

Black to play and save the marked stones.

I was wondering about a double-atari at the 4-5pt but this is not the case:

Just assume all the white stones on the outside are alive

It doesn’t seem possible at the end of the game. If white can ever play M13, white gets an eye vs. no eye and black dies. If black plays M13, white plays N12, after which black can’t play anywhere inside or white can make a killing shape, which sounds like seki, but white has space to make an eye, and as such can get eye vs. no eye and kill black.

That’s pretty much it. There’s a few other ways for black to die, but they all come down to “white can always make a killing shape or else get an eye.” If black had an extra external liberty, he might be able to do something, but that’s a different tsumego.

On an added note, I don’t think white can kill black until after move 53, when there’s only one remaining outside liberty. Black seems to be able to get a ko before then, though I haven’t read the sequence in detail. M12 lives unconditionally for black anytime before then.

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