How Galaxies Puzzles Work

Summary:
Galaxies (also called Tentai Show) is a logic puzzle where you divide a grid into regions, one around each dot, so that every region has 180° rotational symmetry about its dot. This tutorial explains the goal, the symmetry rule, and how to start solving.

Overview

A Galaxies puzzle is a rectangular grid sprinkled with dots. Your job is to draw borders that split the whole grid into regions called “galaxies” — exactly one galaxy per dot. The catch is that every galaxy must be perfectly symmetric: if you spin it 180° around its own dot, it lands back on itself. It is quick to learn, needs no arithmetic, and scales smoothly from a gentle warm-up to a real challenge.

The Goal

Divide the grid into galaxies so that:

Every galaxy contains exactly one dot, and every dot belongs to exactly one galaxy.
Every cell belongs to exactly one galaxy — no cell is left out and none is shared.
Each galaxy is connected — you can walk between any two of its cells without leaving the region.
Each galaxy is point-symmetric around its dot. Rotating the galaxy 180° about its dot produces the identical shape. The dot always sits at the galaxy’s exact centre.

A well-formed Galaxies puzzle has exactly one solution, reachable by logic alone.

Where the Dots Sit

Dots are not always in the middle of a cell. A dot can be placed:

On a cell centre — its galaxy grows outward symmetrically from that single cell.
On an edge between two cells — the smallest possible galaxy is those two cells.
On a corner shared by four cells — the smallest possible galaxy is that 2×2 block.

The dot’s position tells you exactly where the centre of symmetry is, which is the key to every deduction.

How to Start Solving

Claim each dot’s own cells first. A centre dot owns its cell; an edge dot owns the two cells it sits between; a corner dot owns its 2×2 block. These are free.
Use the mirror rule constantly. Whenever you add a cell to a galaxy, its mirror image through the dot must also belong to that galaxy. Cells come in symmetric pairs, so you are really making two moves at once.
Work the edges and corners. A cell in the corner of the grid can only belong to a galaxy whose dot is positioned to keep it symmetric, which sharply limits the options.
Look for cells with one owner. When a cell could only ever be reached symmetrically by one dot, it is forced into that galaxy.
Fill the gaps. Every cell must end up owned. If an empty cell can belong to only one galaxy without breaking another’s symmetry, assign it.
Avoid guessing. Before committing a cell, check that its mirror cell is free and that the move does not strand a cell that no other galaxy can reach.

A quick worked example. Picture a dot sitting on the line between two side-by-side cells. Those two cells are its galaxy’s seed. Now suppose the cell directly above the left seed cell belongs to this galaxy too. The mirror rule forces its partner — the cell directly below the right seed cell — into the same galaxy, because a 180° turn about the dot maps one onto the other. You placed one cell and the symmetry handed you the second. Keep pairing cells this way and the galaxy grows outward in balanced steps until every cell on the board is owned.

Solving – Examples

The example below shows the options for some of the galaxies:

To extend a galaxy, it has to be symmetric. Dot 1 cannot extend to the left or bottom, so it cannot extend to the top or right either.
Dot 2 ditto. It occupies two cells already, it cannot extend to the bottom, so the cells just above cannot belong to this galaxy
Dot 3: This galaxy occupies 2 cells from the start. It cannot extend to the bottom, but it could extend to the sides
Dot 4: a dot occupying 4 cells already. It cannot extend to the top, so the bottom is also fixed. At the left there’s another dot, so only 1 option to grow, which has to grow symmetrically to the right.

Difficulty Levels

Galaxies puzzles in Puzzle Maker Pro use the two difficulty levels:

Normal — solvable by straightforward symmetry deductions, a comfortable everyday level.
Unreasonable — may require chains of reasoning or careful look-ahead to crack.

There are no Easy or Hard levels.

A Friendly Variation: Picture Galaxies

The dots do not have to be plain circles. In Puzzle Maker Pro each dot can be shown as a small picture — for example a different animal at the heart of every galaxy — turning the puzzle into “give each cat its own territory.” The rules are unchanged; the pictures just make the page more inviting, which works well for children’s and themed books.

Outcome

You now understand the goal, the 180° symmetry rule, where dots sit, and the first solving moves. Want to make your own? See How to Create Galaxies Puzzles in Puzzle Maker Pro.