# How does black kill white in this Tsumego?

I'm struggling with "Basic problem #46" from Tsumego Pro. It looks like this, black to play:

``````\$\$ |--------------
\$\$ | . O O . . . .
\$\$ | . . O X X . .
\$\$ | . O O X . X .
\$\$ | X X X O X . .
\$\$ | . . . O . . .
\$\$ | . O O . . . .
\$\$ | . . O . . . .
\$\$ | . . . . . . .
``````

In the built-in "correct" solution, after black takes the vital point, white plays 2 right below, after which a, b, and c all kill white:

``````\$\$ |--------------
\$\$ | a O O c . . .
\$\$ | 1 b O X X . .
\$\$ | 2 O O X . X .
\$\$ | X X X O X . .
\$\$ | . . . O . . .
\$\$ | . O O . . . .
\$\$ | . . O . . . .
\$\$ | . . . . . . .
``````

I don't understand why white would play 2 here, depriving themselves of a liberty. If instead it started the semeai below the three black stones, I'm not able to find a variation where black is able to avoid seki. For example:

``````\$\$ |--------------
\$\$ | . O O 3 . . .
\$\$ | 1 . O X X . .
\$\$ | 5 O O X . X .
\$\$ | X X X O X . .
\$\$ | 6 4 2 O . . .
\$\$ | . O O . . . .
\$\$ | . . O . . . .
\$\$ | . . . . . . .
``````

(3 and 5 could also be in reverse order), or this one:

``````\$\$ |--------------
\$\$ | . O O 7 . . .
\$\$ | 1 . O X X . .
\$\$ | 5 O O X . X .
\$\$ | X X X O X . .
\$\$ | 3 4 2 O . . .
\$\$ | 6 O O . . . .
\$\$ | . . O . . . .
\$\$ | . . . . . . .
``````

If black 3 at 4 then black is dead. If black 5 doesn't happen (either on the 3rd or the 5th move), then either:

``````\$\$ |--------------
\$\$ | a O O 3 . . .
\$\$ | 1 5 O X X . .
\$\$ | . O O X . X .
\$\$ | X X X O X . .
\$\$ | 6 4 2 O . . .
\$\$ | . O O . . . .
\$\$ | . . O . . . .
\$\$ | . . . . . . .
``````

(or 5 at a, or 3 and 5 reversed once more) and black is dead, or:

``````\$\$ 5 anywhere but a, b, or c
\$\$ |--------------
\$\$ | a O O 3 . . .
\$\$ | 1 b O X X . .
\$\$ | c O O X . X .
\$\$ | X X X O X . .
\$\$ | . 4 2 O . . .
\$\$ | . O O . . . .
\$\$ | . . O . . . .
\$\$ | . . . . . . .
``````

and white plays c, killing black. If 3 and 5 are on two of a, b, and c in the last diagram, black is dead once more.

What variation am I missing where black can kill white if white plays this way?

• Is the tsumego actually asking for black to kill? Or is it just looking for a "best move" scenario? Because whether white ends up dead or in seki, black 1 is still the best move here for black (and white is the one who gets to choose the continuation.) Jul 2 '17 at 17:27
• @goldPseudo Just "best move", but generally tsumegos in this collection (and this one in particular) are looking for more than one move. So there are white responses programmed in, and black 1 doesn't make the puzzle "solved" yet. Jul 2 '17 at 17:29
• Surely the solution is just asserting (correctly) the unique black move to get at least a seki. Jul 7 '17 at 0:36