All you need to know about Carpenter's Square - 32
Diagram 32.1: White to play
Because of the external liberty, a ko would be an acceptable outcome for white.
Diagram 32.2: Solution 1
The 
tesuji still works. However because of the external liberty, white can no longer follow the sequence in Diagram 31.3. Please consider what's next?
Diagram 32.3: Solution 1 (continued)
is the magic move. It is amazing that white can arrange to give up 4 stones first ......
Diagram 32.4: Solution 1 (continued)
is an atari so black has to form a ko. This completes the first solution. This also demonstrates that if there are 2 or more external liberties black can live unconditionally using oshi-tsubushi.
Diagram 32.5: Solution 2
This sequence is exactly the same as in Diagram 31.4. This is the second solution.
Conclusion: White has two ways to start a ko fight. The solution in Diagram 32.4 is marginally better for white as both bottom and right sides have already been blocked if black eventually wins the ko.
