All you need to know about Carpenter's Square - 31

Diagram 31.1: White to play

This shape is very similar to Shape 30.

Diagram 31.2: Solution

The solution is similar too. White 1 is still the key point and black corner suffers the same fate as in Shape 30.

Diagram 31.3: Variation

Black 4 does not work either. White has longer liberty. Note that white cannot play Black 6 though.

Diagram 31.4: White fails

White 1 is incorrect. Black 4 is important to form a ko. If black connects at Black 6 first, allowing white to occupy Black 4 , the corner would be dead.

To summarise: this is another simple problem. The tesuji White 1 in Diagram 31.2 should be memorised.