All you need to know about Carpenter's Square - 10

Diagram 10.1: White to play

Black has no external liberties but hanes at both sides. Can white do anything?

Diagram 10.2: Solution

Because of symmetry Black 2 can attach at either side. We've already learned the importance of Black 4 and Black 6 in earlier articles - they both help to keep sufficient eyespace. The result is a 10000-year ko.

Diagram 10.3: Variation

White 5 is incorrect. After White 7 black can safely play elsewhere. White still need to throw in at 'a' to form the 10000-year ko, wasting one move.

Diagram 10.4: Variation

How about White 3 ? Black 6 is a good move. This is a typical seki shape in the corner.

Diagram 10.5: Variation

White 5 is an alternative, after the Black 6 / White 7 exchange, black can play tenuki. This shape is rather interesting: black does not need to do anything; white is unwilling to play 'a' (that would become seki), but before throwing in 'b', white has to reduce black's external liberty first in order to form a direct ko. Because of this nature, I consider this shape also a 10000-year ko, although it does not look like one. Black has two extra moves to prepare the ko fight (for example creating ko threats elsewhere). If black is unhappy to wait and ko-threat situation is appropriate, black can play 'a' immediately, resulting in a 1-move approach ko to his favour.

Generally speaking, with two first-line hanes, white is unlikely to cause black serious troubles. Diagram 10.5 may be white's best chance.