All you need to know about Carpenter's Square - 10
Black has no external liberties but hanes at both sides. Can white do anything?
Because of symmetry can attach at either side. We've already learned the importance of and in earlier articles - they both help to keep sufficient eyespace. The result is a 10000-year ko.
is incorrect. After black can safely play elsewhere. White still need to throw in at 'a' to form the 10000-year ko, wasting one move.
How about ? is a good move. This is a typical seki shape in the corner.
is an alternative, after the / 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.