These problems are about defending weak groups. Sometimes this is a matter of life and death, and sometimes it is merely about avoiding a severe reduction. Always the most profitable move is desired. Please contribute if you have similar problems of your own, or if you know of an existing collection featuring this type of problem.
Problem 1: Black to move
- Click Here To Show Diagram Code
[go]$$c Should black defend the top group? If so, how?
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . O O X . . X O . . . . . . . . |
$$ | . . X O X X . X . X O X . . . . . . . |
$$ | . . X O O O X X X O X O . . . X . . . |
$$ | . . . . . . O O O O . . . . . . . . . |
$$ | . X X O . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Solution – Connecting out
If you're wondering why white allows black to connect under, see below:
Solution – Variation
The sagari at
does not work. Black escapes with 
and white's three stones are lost.
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[go]$$Bc Black skilfully escapes.
$$ ---------------------------------------
$$ | . . . . . . . . . . 3 . . . . . . . . |
$$ | . . X . O O X . . X O 1 . . . . . . . |
$$ | . . X O X X . X . X O X . . . . . . . |
$$ | . . X O O O X X X O B O . . . X . . . |
$$ | . . . . . . O O O O 2 . . . . . . . . |
$$ | . X X O . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |[/go]
If you're wondering why white allows black to connect under, see below:
Solution – Variation
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[go]$$Bc White loses three stones.
$$ ---------------------------------------
$$ | . . . . . . . . . . 2 . . . . . . . . |
$$ | . . X . O O X . . X O 1 . . . . . . . |
$$ | . . X O X X . X . X O X . . . . . . . |
$$ | . . X O O O X X X O X O . . . X . . . |
$$ | . . . . . . O O O O 3 . . . . . . . . |
$$ | . X X O . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |[/go]
The sagari at
does not work. Black escapes with and white's three stones are lost.Problem 2: Black to move
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[go]$$c Should black defend the top group? If so, how?
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . O O X . . . . . . . . . . . . |
$$ | . . X O X X . X . X O . . . . . . . . |
$$ | . . X O O O X X X O X . . . . X . . . |
$$ | . . . . . . O O O O . . . . . . . . . |
$$ | . X X O . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Solution
Black must make eyes directly.
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[go]$$Bc Black is fully settled.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . O O X . 3 . 1 . . . . . . . . |
$$ | . . X O X X . X . X O 2 . . . . . . . |
$$ | . . X O O O X X X O X . . . . X . . . |
$$ | . . . . . . O O O O . . . . . . . . . |
$$ | . X X O . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |[/go]
Black must make eyes directly.
Problem 3: Black to move
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[go]$$c Should black defend the upper left? If so, how?
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O X X . X O . . . . . . . . . . |
$$ | . . . O . O X . O , . . . . . X . . . |
$$ | . . O . . O X . . . . . . . . . . . . |
$$ | . X X O . . O . . . . . . . . . . . . |
$$ | . . . X O . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . O . . . . X . O . . . |
$$ | . . . . . . . . . . O . O X . . O . . |
$$ | . . . O . . . . . X O . O . . X O . . |
$$ | . . . . . X . . X . X X . . X . X O . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Solution
Failure 1 – Living small
Failure 2 – Tenuki
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[go]$$c Black runs with
while splitting white.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O X X . X O . . . . . . . . . . |
$$ | . . . O . O X . O , . . . . . X . . . |
$$ | . . O . . O X 1 . . . . . . . . . . . |
$$ | . X X O . . O . . . . . . . . . . . . |
$$ | . . . X O . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . , . . . |[/go]
Failure 1 – Living small
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[go]$$Bc Black lives, but white gets superior thickness.
$$ ---------------------------------------
$$ | . . 8 7 . . . . . . . . . . . . . . . |
$$ | . . 6 5 . 9 . 3 1 2 . . . . . . . . . |
$$ | . . . O X X . X O . 4 . . . . . . . . |
$$ | . . . O . O X . O , . . . . . X . . . |
$$ | . . O . . O X . . . . . . . . . . . . |
$$ | . X X O . . O . . . . . . . . . . . . |
$$ | . . . X O . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . , . . . |[/go]
Failure 2 – Tenuki
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[go]$$Wc
threatens the killing move of a – white must live as in Failure 1.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . a . . . . . . . . . . |
$$ | . . . O X X . X O . . . . . . . . . . |
$$ | . . . O . O X . O , . . . . . X . . . |
$$ | . . O . . O X . . . . . . . . . . . . |
$$ | . X X O . . O 1 . . . . . . . . . . . |
$$ | . . . X O . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . , . . . . . , . . . |[/go]
Problem 4: White to move
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[go]$$c Should white defend the upper right? If so, how?
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . O . O O O O X . . . |
$$ | . . . O . . . . . , . X O X . X . O . |
$$ | . . . . . . . . . . . . X X . X . . . |
$$ | . . . . . . . . . . . . X O . O O . . |
$$ | . . . . . . . . . . . . . O . O . . . |
$$ | . . . . . . . . . . . X . . X X O O . |
$$ | . . . . . . . . . . . . X . . . X X . |
$$ | . . . . . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . O . . . |
$$ | . . . . . . . . . . . . . X . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Solution 1 – Tenuki
is the only move big enough to justify tenuki (under modern rulesets – a is better if there is a group tax). Black can reduce white in sente as shown, but white is now alive. Even if black plays at b next, white can still make two eyes.
Solution 2 – Kosumi-Tsuke
helps white settle the corner while threatening to connect. Although white ends in gote, the balance of territory is much more in white's favor locally.
Failure – Keima
might come to mind as another move that threatens to connect, but in this case it is a failure.
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[go]$$Wc White is reduced, but is adequate compensation.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . O . O O O O X 4 2 . |
$$ | . . . O . . . . . , . X O X . X 3 O . |
$$ | . . . . . . . . . . . . X X . X . b . |
$$ | . . . . . . . . . . . . X O . O O . . |
$$ | . . . . . . . . . . . . . O . O . 5 . |
$$ | . . . . . . . . . . . X . . X X O O . |
$$ | . . . . . . . . . . . . X . . . X X . |
$$ | . . . . . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . a . . . |
$$ | . . . . . . . . . . . . . . . . 1 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . O . . . |
$$ | . . . . . . . . . . . . . X . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
is the only move big enough to justify tenuki (under modern rulesets – a is better if there is a group tax). Black can reduce white in sente as shown, but white is now alive. Even if black plays at b next, white can still make two eyes.Solution 2 – Kosumi-Tsuke
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[go]$$Wc White is comfortable.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . 2 3 . |
$$ | . . . . . . . . . O . O O O O X 1 7 . |
$$ | . . . O . . . . . , . X O X . X 6 O . |
$$ | . . . . . . . . . . . . X X . X 5 4 . |
$$ | . . . . . . . . . . . . X O . O O . . |
$$ | . . . . . . . . . . . . . O . O . . . |
$$ | . . . . . . . . . . . X . . X X O O . |
$$ | . . . . . . . . . . . . X . . . X X . |
$$ | . . . . . . . . . , . . . . . , . . . |[/go]
helps white settle the corner while threatening to connect. Although white ends in gote, the balance of territory is much more in white's favor locally.Failure – Keima
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[go]$$Wc White fails to connect.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . 1 . . |
$$ | . . . . . . . . . O . O O O O X 3 2 . |
$$ | . . . O . . . . . , . X O X . X 6 O . |
$$ | . . . . . . . . . . . . X X . X 5 4 . |
$$ | . . . . . . . . . . . . X O . O O . . |
$$ | . . . . . . . . . . . . . O . O . . . |
$$ | . . . . . . . . . . . X . . X X O O . |
$$ | . . . . . . . . . . . . X . . . X X . |
$$ | . . . . . . . . . , . . . . . , . . . |[/go]
might come to mind as another move that threatens to connect, but in this case it is a failure.