Group With Most Liberties

    Keywords: Shape

What is the most liberties a _single_ group can have on a standard goban?

The first guess one might make is concentric squares as shown in:


This results in 226 liberties. There are 11 wasted points and 4 stones with only a single liberty.

A little bit of playing around results in some different shapes generating more liberties:

[ext] [ext]

Both of these have 229 liberties with 2 wasted squares and 11 stones only having 1 liberty.

The question is, is there any group with 230 or more liberties?

tapir: It would be lovely, if instead of pictures hosted elsewhere, you could use diagrams native to Sensei's Library. See: How Diagrams Work.


19x19 diagram  

Dieter: My first idea was a spiral

  • Stones: 18+16+16+13+13+10+10+7+7+4+4+2 = 120
  • Wasted points: 12
  • 361-132=229
  • Corners serving as double liberties: 11; plus 1 at the tail.

I have a strong indication that 229 is the maximum but I cannot prove it.

Group With Most Liberties last edited by Dieter on November 20, 2013 - 16:44
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