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I switched starting array both sides A and B as intended, with the 'B's
initially cornered for better action.  'B' at 4 cannot move to 2, only 1 and 9, because that is
where one or two borders away go; Triangle 2 would be 3 external sides removed
from 4 and illegal. Also any 1,5,9 is Double Adjacency at start or finish
of any turn by notional externalities. That should be it for Tetraktys. 
More cells, triangles, would be interesting up to a point. Five stars add 7 cells for 16-triangle board. Then six stars add 9 more cells for 25-triangle board. Then seven stars add 11 more cells for 36, eight 13 for 49, nine 15 for 64 triangles. Q.E.D. These would not be for large or normal Chess-like game just the limited study ones, because the outside moving, enhancing up to 25 or 36, starts getting distracting and artificial. Potential thousands of non-trivial games exist on nested equilateral triangular sizes 16 through 49, latter eight-starred. Please proliferate in kind.