Normal sudoku rules apply. Divide the grid into galaxies: orthogonally connected groups of cells that have 180 degree rotational symmetry about their centers (marked with a small dot). All cells must be part of a galaxy; no galaxies overlap. Galaxies are either red-shifted (moving away from the observer), or blue-shifted (moving towards the observer). The measured value of each galaxy is shown; it is the sum of the digits in that galaxy PLUS (blue-shifted) or MINUS (red-shifted) the number of cells in the galaxy. Dots with a solid black outline indicate "Renban" galaxies, whose digits form an unbroken consecutive sequence in any order. Conversely, dots without a solid black outline indicate galaxies whose digits do NOT form such a sequence. Digits may not repeat within a galaxy. Five single-cell galaxies — "Dark Stars" — are NOT marked: their locations must be deduced by the solver. All cells (max 8) around a Dark Star belong to regular galaxies. No 3x3 box contains more than one Dark Star. Digits do not repeat amongst the Dark Stars.
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