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This is a generalization of a puzzle which appeared on Ed Pegg's mathpuzzle.com

For another of his puzzles, see Cross Prime

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Select some of the small triangles to shade (change color) by clicking on them. Click again to 'un-shade' (change color back).

The object is select a subset for shading, such that each vertex is adjacent to the same number of shaded triangles. (Choose the number: 1, 2, or 3).

Vertices with such adjacency lose their blue circle.
When there are no more blue circles, the puzzle is solved !

I have found one solution (except for symmetry) for Adjacency=1, two for Adjacency=2 (not counting the outer 'corners'), and either the interior or the border for Adjacency=3.
What are your results (if they differ) ?