All you need to know about Carpenter's Square - 20
Diagram 20.1: White to play
Does 
help in any way?
Diagram 20.2: False hope
is incorrect. Black is expecting this sequence similar to Diagram 19.2. would help in this case. However......
Diagram 20.3: Black fails
is the correct answer. Note that white can use this sequence in Shape 19 as well.
Diagram 20.4: Continued (12=
, 13= 
)Black is one liberty too short and cannot play 'a'.
Diagram 20.5: Black fails
So black has to block at . However, 
is incorrect. This result is the same as Diagram 19.3 and black fails to make use of .
Diagram 20.6: Solution 1
Unlike Diagram 19.4, tesuji now works. Thanks to black can throw in 
to start a ko fight.
Diagram 20.7: Variation
may atari from the other side, forming a different ko. But note that black takes the ko first so this result cannot be good for white.
Diagram 20.8: Solution 2
Since in the previous diagram appears to be the key point, 
wants to occupy that location first. To avoid the failure in Diagram 20.5, is a must. is a nice idea. Black has to go back to to avoid the Bulky Five killing shape. So the result is a ko. If black wins the ko fight by connecting at , white can still play 'a' to form a seki, destroying 9 points of territory, although black also has a yose at 'b' that can get a few points back. Overall this solution seems to be slightly worse than Solution 1 for black.
Diagram 20.9: White fails
is a thoughtless move, hoping black to block at 'a' so that knowledge in Shape 7 can apply. But is good - please verify that black is unconditionally alive now.
To summarise: black corner is quite resilient because of the hane move. Diagram 20.6 and Diagram 20.8 are the right solutions, resulting in ko.
