All you need to know about Carpenter's Square - 21
Diagram 21.1: Black to play
Let us discuss this corner shape seemingly weakened by 
. Suppose white just plays 
, how can black respond?
Diagram 21.2: White fails
is incorrect, but 
is wrong too. 
is the key point and black is alive.
Diagram 21.3: Black fails
occupies the key point instead. is the most tricky answer (clearly 
or 
not working). Although 
is a good move (a common tesuji to avoid those big-eye killing shapes), it doesn't work here......
Diagram 21.3: Black fails (continued)
is a calm move. Black is killed.
Diagram 21.4: Solution
It becomes clear now that is the key point. If white plays , black has a number of forcing moves, followed by .
Diagram 21.5: Solution (continued)
can be a tesuji sometimes. But because of the external liberty at 'a', black can use Oshi-tsubushi tesuji to kill the white stones.
Diagram 21.6: Black fails
also looks like a key point, but so is . If black chooses 
, white can form almost a picnic ko. Black clearly fails.
Diagram 21.7: Black fails too
here is better. After there is just enough room for black to make two eyes. Black is successful in a pure life & death sense. But comparing to Diagram 21.4, black is almost 10 points worse off so I cannot accept this as an alternative solution.
Diagram 21.8: White fails
is slightly more challenging. 
is incorrect. Black can play and the corner is completely alive.
Diagram 21.9: Same as Diagram 21.6
Apparently is the key point. This results the same as Diagram 21.6.
Diagram 21.10: Black fails
doesn't work and the corner is killed by 
.
Conclusion: Diagram 21.4 is the only right solution. Luckily it is not hard to memorise that: is almost always the key point for Carpenter's Square shapes.
