Galaxies (Spiral Galaxies) Puzzle

Galaxies is a region puzzle, also called Spiral Galaxies. You draw walls on the edges of a grid so the cells split into galaxies. Each galaxy has one dot, and the shape is symmetric about that dot. You can play 5×5 through 10×10, plus a 6×8 rectangle, each in easy, medium, and hard. Every puzzle here has exactly one solution.

Rules

The board is a grid of cells. A thick frame runs around the outside and counts as a wall. Thin lines show the interior edges, which are the ones you mark. Dots are drawn on top. A dot may sit at a cell centre, at the middle of an edge, or at an interior corner.

The rules are these three. Each region has exactly one dot. A region looks the same after a half-turn about its dot. Every cell belongs to a region.

A half-turn spins the region 180 degrees around its dot. Every cell in the region must land on another cell in the same region. A cell-centre dot can own a single cell. An edge dot needs a pair of cells that mirror across that edge. A corner dot needs a block that mirrors across that point.

A wall on an edge separates two galaxies. You cannot draw a wall through a dot. An open mark, drawn as a small ×, means you believe the two cells stay in the same galaxy. Open marks are notes. They do not have to be filled in, and they do not have to be cleared when the walls are right.

A region that is already closed is checked at once. A closed region with no dot, a closed region with two or more dots, or a closed region that is not symmetric about its dot is a clash. An open mark that is the only join between two finished galaxies is a clash as well. An edge you have not decided yet stays quiet.

The puzzle is solved when the walls are the borders of the unique set of galaxies. The outer frame is part of that border. Open marks are ignored.

Controls

Wall and Open sit under the board. Wall mode cycles an edge from empty to a wall and back to empty. Open mode cycles an edge from empty to an × and back to empty. Tap the same mark again to clear it. Right-click, or press and hold, places the other mark once.

The arrow keys move an edge cursor. The cursor starts on the first interior edge. Space or Enter places a wall on the cursor. X places an open mark. Backspace or Delete clears the edge. M switches between Wall and Open.

Press Hint for one edge the rules already force, with a sentence saying why. The hint highlights the cell, its partner, the dot, and the edge it decides. Press Check when you want the board checked against the rules. Undo and Redo step through your moves, and Reset clears every mark. When the walls are complete and legal, the board turns teal.

A coral edge or cell is a clash that is already visible: a wall through a dot, a closed region with the wrong number of dots, a closed region that is not symmetric, or an open mark between two finished galaxies.

Techniques

Easy grids follow from the cells a dot already owns:

• Home: the dot already owns the cells it sits on, so the edges inside that pair or block stay open and the far edges become walls when the shape is only those cells.
• Only one centre: a cell that only one dot can cover is given to that dot, and its partner comes with it.
• Reach: a cell that touches one galaxy, and that no other galaxy can reach, joins that galaxy.
• Far reach: a cell that only one galaxy can reach joins it, even before they touch, and its partner comes with it.

Medium grids add one more step:

• Bridge: if a cell is the only link that keeps a galaxy in one piece, that cell must join the galaxy.

Hard grids also ask you to test a centre:

• Try a centre: assume a cell belongs to one dot and follow the steps above. If that leads to a broken rule, the cell belongs to another dot.
• Agree: whichever centre you assume, any edge or cell that comes out the same every time is fixed.

Beginner tips

Start with a dot on an edge or a corner. That dot already owns two or four cells, so the wall around that small block is often the first line you can draw.

When a cell has only one possible centre, place it and its partner together. The partner is the cell you land on after a half-turn about the dot.

If you are new to Galaxies, start with a 5×5 easy grid, or the daily 7×7 easy grid, and move up once the half-turn feels natural. Play runs from Easy → Hard on every size from 5×5 to 10×10 and on 6×8.