The rules of Tentai Show
Tentai Show — 天体ショー — or Spiral Galaxies is a symmetry puzzle.
- Divide the whole grid into regions called galaxies. Every cell belongs to exactly one.
- Each galaxy is a single connected piece — you can walk between any two of its cells without leaving it.
- Each galaxy contains exactly one dot, and that dot is its centre of symmetry. Turn the galaxy half a turn about its dot and it lands on itself.
- A dot in the middle of a cell, on the line between two cells, or on a corner where four meet — all three are allowed, and each tells you something about the shape.
Ways in
Read the dots before you draw
A dot on an edge or a corner tells you the galaxy is even in that direction, which rules out a whole class of shapes. Doing this for every dot first often fixes several boundaries for free.
Work in pairs
Assigning a cell to a galaxy immediately assigns its opposite number about the dot. If that opposite cell is off the grid, or already belongs to something else, the assignment was impossible — which is usually how you eliminate a candidate.
Adjacent dots divide
Two dots in neighbouring cells cannot share a galaxy, so the line between them is a boundary. This is the standard opening and often the only free move on a hard grid.
Corners are forced
A cell in the corner of the grid can only be reached by galaxies whose dot is positioned so the opposite cell also lands on the board. On a big grid that is often a single candidate.
Watch for stranded cells
If a cell can only be reached by one galaxy without cutting another galaxy off from its dot, it belongs to that one. Connectivity does as much work here as symmetry.