Which sun and ring take 3 planets

Every cell is a sun and a ring whose difference is even, so a whole planet fits between them and the drawing can be made. Shading is what happens when the second planet is asked for. Green assembles; grey fails the divisibility condition, which says the sun and ring teeth must add to a multiple of the planet count; pale fails the neighbour condition, where the planets would touch. Of 1251 cuttable designs, 417 — 33.3% — will actually take 3 equally spaced planets. The condition that removes most of them is arithmetic and appears in no drawing.