Mirror Universe / Star Battle Relay 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, a shading mode, and a shape (star) entry mode for the relay puzzle.)

Theme: Logical

Author/Opus: This is the 37th puzzle from our contributing puzzlemaster Carl Worth.

Rules: First, solve the top grid puzzle as a Mirror Universe puzzle: Divide the grid along the indicated lines into connected regions – “galaxies” – so that every cell is part of one galaxy and every galaxy has one circle clue inside it. If the galaxy contains a plain circle without any lines, the galaxy must be rotationally symmetric with that circle being the center of rotational symmetry. If the galaxy contains a circle with a horizontal, vertical, or diagonal line, the galaxy must have mirror symmetry when reflecting across the line given in the circle. Also, some cells contain black dots – “asteroids” – which must be symmetrically arranged based on the rules of symmetry (rotational or mirror) for every galaxy that contains them.

Mirror Universe + Asteroids Example by Carl Worth:

Then, copy all ten of the galaxy regions from the solved Mirror Universe into the bottom grid. Solve this puzzle as a Star Battle puzzle with two stars in every row, column, and region.

Answer String: For each row from top to bottom, enter the number of the first column from the left where a star appears. Enter these numbers as a single string with no separators.

Time Standards (highlight to view): Grandmaster = 8:00, Master = 10:15, Expert = 20:30

Solution: PDF

Note: Follow this link for other classic Star Battles. If you are new to this puzzle type, here are our easiest Star Battles to get started on. More Star Battle puzzles can be found in The Art of Puzzles and in our beginner-friendly collection Intro to GMPuzzles by Serkan Yürekli.

• Grizix says:

Wow, amazing puzzle(s) !
Didn’t see the 28 minutes pass.
Although, I did not manage to find a logical way to finish the last steps of the Star Battle…

• Carl W says:

I really like constructing relay puzzles for some reason. (And it might be that this puzzle provided the motivation for me to add the “asteroid” element to Mirror Universe. That allows for targeting galaxy shapes that would be hard to force otherwise. And fortunately, the asteroid element works well for its own sake.)

As for the logical path on the Star Battle, I know it must be there because I know I constructed that in a forward direction by hand. But I’ll have to go re-solve this because I honestly don’t remember the solving path at this point, (I constructed this quite a while ago).

• Ryan Tamburrino says:

Carl, do the mirror symmetry circle clues have to be at the center of symmetry/reflection? For example, if the example you show here, is it possible for the circle clue in the top right region to be in the topmost, rightmost square?

• drsudoku says:

Hi Ryan — the galaxies with rotational symmetry always have the circle at the center of rotational symmetry. The galaxies with mirror symmetry always have the circle clue along the axis of mirror symmetry.

• Ryan Tamburrino says:

Thanks! I solved it quickly after that misconception was cleared up.

• str says:

This was a very cool puzzle! Thank you Carl!

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