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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

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

What are your results (if they differ) ?