Carpenter's Square - Wrong Attack

How to answer 1?  

Recall that the status of the carpenter's square is a ko, when is played at a.

here is a wrong attack on the carpenter's square. Why?

Solution  

The descent at is the solution. It gurantees unconditional life (which includes seki, of course).

Solution (easy variation 1)  

If , then onwards result in a seki.

Solution  

If here, then the placement at is a tesuji.

If at a, then White at , Black b, White c connects and kills Black at the same time.

Solution (easy variation 2)  

connects, and forms a seki.

Solution (main line)  

The main line starts with . is the only move.

If is played at a, then White 5, and Black dies (eyes win capturing races).

On the other hand, if is played at a, then Black b is an atari in sente, forcing White c, and Black d makes two eyes.

Solution (main line)  

Hence, the main line continues with capturing two Black stones. To avoid having White having an eye that wins the capturing race, and are vital. White can only connect underneath at .

Solution (main line)  

The finalle is the capture at , living because two White stones are also captured via connect and die.

Failure  

The throw-in at is a failure. captures the stone, and if Black a, then White b. Black's mistake is punished by shortage of liberties.