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or solve online (using our beta test of Penpa-Edit tools; use tab to alternate between a composite mode for line/edge drawing and a number entry mode.)

Theme: Clue Symmetry and Logic

Author/Opus: This is the 36th puzzle from our contributing puzzlemaster Carl Worth.

Rules: Combination of Spiral Galaxies and Fillomino rules. Divide the grid along the dotted lines into regions, each of which must contain either exactly one circle, or one or more identical given numbers. (Note that there are no “hidden polyominoes” in this puzzle meaning there are no regions without a given number or a given circle.) Each region containing a circle is a “galaxy” and must have rotational symmetry with the circle at its center. Each region with given numbers must be the same size in cells as those numbers. Two regions with numbers of the same size cannot share an edge, but a region with numbers and a region with a circle in it can be the same size.

Answer String: For each cell in the marked rows, enter the area of the region it belongs to. Enter just the last digit for any two-digit number. Start with the 4th row, followed by a comma, followed by the 8th row.

Time Standards (highlight to view): Grandmaster = 7:00, Master = 13:45, Expert = 27:30

Solution: PDF

Note: Follow this link for classic Spiral Galaxies puzzles on this website and this link for variations on Spiral Galaxies puzzles. If you are new to this puzzle type, here are our easiest Spiral Galaxies Puzzles to get started on. More Spiral Galaxies puzzles can be found in The Art of Puzzles 2.