All you need to know about Carpenter's Square - 27

Diagram 27.1: White to play

Can Black square secure this corner?

Diagram 27.2: White fails

White 1 appears to be important, but White 5 can only start a ko here.

Diagram 27.3: White fails

White 5 has the option to fight an alternative ko. This way white takes the ko first which is a slight improvement.

Diagram 27.4: Solution

Making White 1 / Black 2 exchange first is the correct order. Then white can come back to the key point White 3 and kill the corner - black cannot play 'a'.

Conclusion: Diagram 27.4 is a simple and elegant solution.