ConstructionProblem3/Solution

Consider possibilities for white stones only. Categorize per number of strongly connected stones.

The answer is 23

Carré (1)  

Connected four with three in a line(4)  

Twisted four (1)  

Straight triplet (2)  

Bent triplet (5)  

Double pair (3)  

Pair and two singles (4)  

all singles (3)