# Shapes related to the carpenter's square

Keywords: Life & Death

## Shape 1

### No outside liberties

Shape 1

Without outside liberties, White can kill by a ko.

Ko

The ko sequence.

Variation

is an interesting resistance, but ensures a ko.

```But what about:
```
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 a outside liberty, the result is still a ko.

Example sequence

This is an example sequence.

## Shape 2

### No outside liberties

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 form an eye at a.

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

### With outside liberties

Shape 2

Without outside liberties, White can still get a ko.

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

### With an open side

Shape 3
Proposal

BramGo: Is this correct?

B cannot win the liberty race

With no outside liberties on the 4th-line L group, W can kill without needing a descent to the second line.

Without an outside liberty, the best that W can get is a ko, by forming the carpenter's square.

The above is not correct. See L-group on the 4th line.

## Carpenter's Square with an extra leg

Black is alive in seki
Black is alive.
Failure: defending from the wrong side leads to a ko.