Life In 19x19

In James Davies Tesuji there is a particular problem regarding a capture race:

White to play

Click Here To Show Diagram Code

[go]$$W
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . X . . |
$$ . . , . O O X X X . . . |
$$ . . O O X X O O X O X . |
$$ . . O X . X . O O X X . |
$$ . . . . . . . . . . . . |
$$ ------------------------+[/go]

The solution given is :

Click Here To Show Diagram Code

[go]$$W
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . X . . |
$$ . . , . O O X X X . . . |
$$ . . O O X X O O X O X . |
$$ . . O X . X . O O X X . |
$$ . . . 5 3 2 1 . 4 . . . |
$$ ------------------------+[/go]

Where 2 and 3 are miai (maybe I am not understanding this).

I can't quite see what the solution would be if Black played :

Click Here To Show Diagram Code

[go]$$W
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . X . . |
$$ . . , . O O X X X . . . |
$$ . . O O X X O O X O X . |
$$ . . O X . X . O O X X . |
$$ . . . . 2 . 1 . . . . . |
$$ ------------------------+[/go]

If White then plays black can just counter with . Now White cannot play the marked point due to a shortage of liberties:

Click Here To Show Diagram Code

[go]$$W
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . X . . |
$$ . . , . O O X X X . . . |
$$ . . O O X X O O X O X . |
$$ . . O X . X M O O X X . |
$$ . . . . 2 3 1 . 4 . . . |
$$ ------------------------+[/go]

Black then wins the capture race :

Click Here To Show Diagram Code

[go]$$W
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . X . . |
$$ . . , . O O X X X . . . |
$$ . . O O X X O O X O X . |
$$ . . O X . X . O O X X . |
$$ . . 5 7 2 3 1 8 4 6 . . |
$$ ------------------------+[/go]

If White tries to come in from the other side, they still lose :

Click Here To Show Diagram Code

[go]$$W
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . X . . |
$$ . . , . O O X X X . . . |
$$ . . O O X X O O X O X . |
$$ . . O X . X . O O X X . |
$$ . . 3 5 2 7 1 8 4 6 . . |
$$ ------------------------+[/go]

Not quite sure what I am missing. Is there a problem with the problem or a problem with my problem solving?

I think your analysis is correct.

I think that after White 1 Black 2, the right move for White is to play at Black 4.

Pio2001 wrote:I think that after White 1 Black 2, the right move for White is to play at Black 4.

Click Here To Show Diagram Code

[go]$$W
$$ . . . . . . . . . . . . |
$$ . . . . . . . . . X . . |
$$ . . , . O O X X X . . . |
$$ . . O O X X O O X O X . |
$$ . . O X . X 4 O O X X . |
$$ . . . . 2 . 1 . 3 . . . |
$$ ------------------------+[/go]