Shapes related to the carpenter's square

Shape 1  

Without outside liberties, White can kill by a ko.

Ko  

The ko sequence. at a also leads to ko.

Variation  

should just die.

Black mistake  

is a mistake. The result is one eye to none, Black cannot approach and loses the capturing race.

Black mistake  

is wrong. After , and are miai, Black is dead.

White mistake  

cannot kill, the result is a seki. The reader may verify that at a does not work either.

With outside liberties

Shape 1  

With an outside liberty, the result is still a ko.

Example sequence  

This is an example sequence.

Shape 2  

This one looks alive. But without outside liberties, White can kill.

Killing sequence  

White makes use of Black's shortage of liberties with and .

No eye  

If here, then after , Black cannot play at a.

Also dead  

If makes an eye here, then is atari, which allows White to destroy the eye at the corner.

With outside liberties

Shape 2  

With outside liberties, White can still get a ko. (same as Gokyo Shumyo, Section 3, Problem 78).

Ko  

clamping at the 1-2 point is the tesuji that allows White to kill by a ko. If at a, the at b is also a ko.

White mistake  

Connecting underneath at allows to live without ko.

Shape 3  

For a detailed analysis of this position, see L-group on the 4th line.