Tsumego problem

[Ian Butler]

I came up with the following problem while doing some variations of corner approaches/invasions.

White to play and live. (if at all possible. I'm starting to think it's not, not even a ko for life).

[Knotwilg]

I think it can. Haven't checked all options yet, but I see a clear starting move, two possible answers by Black: in one, White lives, in the other, White lives or escapes.

[Ian Butler]

I think it can. Haven't checked all options yet, but I see a clear starting move, two possible answers by Black: in one, White lives, in the other, White lives or escapes.

Care to share the answer?

[Joaz Banbeck]

IMHO, white plays R3 and lives - without even needing a ko.

The R2 stone is then trapped. ( It can connect out, but then, due to the two outside white stones, it and its rescuers die. ) So one eye is at R2.

There are two options for the second eye: S4 and T1. White can get the S4 eye by playing S5, or the T1 eye by playing S2. Black cannot prevent both.

[Knotwilg]

Joaz seems to be right. I thought hane at S5 was a necessary preparation (and possibly sacrifices a part) but it isn't. Here's the main line:

$$W White lives
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . X . . . |
$$ . . . . . . . . X 2 . |
$$ . . . . O 4 X X O . . |
$$ . . . . O X 3 O 1 O 7 |
$$ . . . . . X O . X 8 6 |
$$ . . . . . a 9 . b 5 . |
$$ ----------------------

Click Here To Show Diagram Code

[go]$$W White lives
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . X . . . |
$$ . . . . . . . . X 2 . |
$$ . . . . O 4 X X O . . |
$$ . . . . O X 3 O 1 O 7 |
$$ . . . . . X O . X 8 6 |
$$ . . . . . a 9 . b 5 . |
$$ ----------------------[/go]

5 is crucial. Later, a is sente for b and it's seki.

$$W White lives
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . X . . . |
$$ . . . . . . . . X 2 . |
$$ . . . . O 4 X X O . . |
$$ . . . . O X 3 O 1 O . |
$$ . . . . . X O . X 7 . |
$$ . . . . . . 6 a b 5 . |
$$ ----------------------

Click Here To Show Diagram Code

[go]$$W White lives
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . . . . . |
$$ . . . . . . . X . . . |
$$ . . . . . . . . X 2 . |
$$ . . . . O 4 X X O . . |
$$ . . . . O X 3 O 1 O . |
$$ . . . . . X O . X 7 . |
$$ . . . . . . 6 a b 5 . |
$$ ----------------------[/go]

If Black 6 hane, White makes it easy with 7: next if Black a, White b creates shortage of liberties.