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 White 1 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)

White 7 is the magic move. It is amazing that white can arrange to give up 4 stones first ......

Diagram 32.4: Solution 1 (continued)

White 13 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.