### Double Spiral Galaxies by Carl Worth

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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 shading mode.)

Theme: Double Spiral Galaxy (the pattern of galaxies is a double spiral as shown here)

Author/Opus: This is the 25th puzzle from our contributing puzzlemaster Carl Worth.

Rules: Variation of Spiral Galaxies. In addition to the standard rules, some circles are shaded gray and must belong to galaxies containing two gray circles, not one, with the circles in rotationally symmetric spots for those galaxies.

Answer String: Enter the number of cells in each connected group (between bold lines) in the marked rows. Separate each row’s entry from the next with a comma. The example has the answer “52,11131”.

Time Standards (highlight to view): Grandmaster = 10:30, Master = 17:00, Expert = 34:00

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 will soon be found in The Art of Puzzles 2.

• Nathan says:

Found this really frustrating, just couldn’t follow clean solve all the way through. Near end just had to do trial and error going quite deep before finding the solution. Would love to see video explanation of solve path of this in future, hoping I’m just missing some clever techniques!

• Carl W says:

Nathan, if it helps you feel any better, when I revisited this now, (nearly 2.5 years since I constructed it), it took me _forever_ to find the solving path. It’s definitely a narrow path near the end.

But there does exist a logical step at every point, (without requiring any deep trial-and-error).

I’ll illustrate one step below that will hopefully give you a feel for what the puzzle allows.

Consider the puzzle from this position (SPOILER ALERT: Link leads to an image of a partial solution): https://cworth.org/cworth/tmp/spiral-galaxy-2017-07-01-partial-solution.png

Sebz guvf cbvag, pbafvqre gur gjb funqrq pvepyrf ng ebjf guerr naq sbhe bs pbyhza gjryir. Pbhyq gurfr gjb pvepyrf orybat gb gur fnzr tnynkl? Vs gurl jrer, jung cbgragvny tnynkl pbhyq cbffvoyl ernpu gur pryy ng ebj guerr pbyhza ryrira? Lbh fubhyq or noyr gb pbaivapr lbhefrys gung ab cbgragvny tnynkl pbhyq ernpu gung pryy, fb gurfr gjb pvepyrf zhfg orybat gb frcnengr tnynkvrf.

Sebz gurer, lbh jvyy dhvpxyl pbzovar gur pvepyr ng ebj guerr naq pbyhza gjryir jvgu gur pvepyr ng ebj guerr naq pbyhza guerr. Naq lbh jvyy nyfb pbaarpg gur pvepyr ng ebj sbhe naq pbyhza gjryir jvgu gur pvepyr ng ebj svir naq pbyhza gra.

Gur chmmyr pbagvahrf jvgu fvzvyne fgrcf, jurer pbafvqrevat cbgragvny pbzovangvbaf bs pvepyrf jbhyq vfbyngr na haernpunoyr pryy, (be vfbyngr n funqrq pvepyr) fhpu gung pbzovangvbaf pna or ryvzvangrq naq gur pbeerpg pbzovangvbaf pna or qrgrezvarq.

Vs gur rkcynangvba nobir vfa’g rabhtu gb chfu lbh cnfg lbhe fgvpxvat cbvag, yrg zr xabj naq V pna cebivqr fbzr shegure qverpgvba.

Gunaxf sbe tvivat zl chmmyr n gel, naq V ubcr vg jnf creuncf rayvtugravat rira gubhtu vg jnf sehfgengvat!

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