All you need to know about Carpenter's Square - 28

Diagram 28.1: White to play

Can the external liberty make any difference?

Diagram 28.2: White fails

The external liberty is clearly helpful. If white applies the solution of Shape 27, black is able to play Black 8 so the corner is alive. White has to change strategy.

Diagram 28.3: White fails

White 1 is the key point. However, White 3 is incorrect. Black 4 is again a calm move. Black is alive. If Black 4 mistakenly plays at Black 6 first, then a ko fight in inevitable.

Diagram 28.4: White fails

White 3 doesn't work either. Black 6 is good. Please verify the corner is alive.

Diagram 28.5: Solution

White 3 is a brilliant move, forming a ko fight easily.

Diagram 28.6: Variation

Black 4 is useless. Black can only create a different ko fight, which is favourable for white because white takes the ko first.

Conclusion: Diagram 28.5 is the best for both sides.