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Diagram 7.1: White to play
  
Black has one extra stone at  . Does it help? 
 
  Diagram 7.2: Solution 1
  
  is still the key point. 
It is possible for black to play   now because with   
there black has the leisure to play  . This results in a ko fight. 
I recommend this sequence to beginners as moves here look straight-forward and easy to understand. 
 
  Diagram 7.3: Solution 2
  
If   attaches from the bottom side, 
white can use this standard sequence (explained in Diagram 2.2 in Shape 2). 
It doesn't feel right as black does not make use of   in any way, 
although this result is probably no worse than Solution 1.   
 
  Diagram 7.4: Solution 3
  
Black can also attach from the other side. 
  is an important move, preventing white from playing there to reduce the eyespace. 
The resulting ko is similar to that shown in Diagram 3.5 in Shape 3. 
Again   does not seem to contribute anything. 
 
  Diagram 7.5: Solution 4
  
Black may also attempt to improve the eyespace at  . 
As mentioned   is the key point. 
Black has to form an eye at  
to avoid Bulky Five, leaving a ko fight. Some sources (such as Chen 
Zhigang's article in Weiqi Tiandi magazine) argue that this ko fight is 
less favourable for black, probably because black eventually has to fill
in the corner twice to avoid seki after winning the ko. However, note 
that the  
stone is not necessarily there in real games, so it may not be easy for
white the seal the group from that side (in Solution 3 white has 
already got that side sealed with  ). 
 
  Diagram 7.6: White fails
  
If white misses the key points (  in previous diagram), the results would be much worse. 
This is so-called 10000-year ko. With two extra liberties at   
white has little hope to start a ko and is more likely to settle in seki. 
 
To summarise, surprisingly for black the extra hane helps very little. Ko is still the normal outcome. 
 
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