Tentai Show

The rules of Tentai Show

Tentai Show — 天体ショー — or Spiral Galaxies is a symmetry puzzle.

  1. Divide the whole grid into regions called galaxies. Every cell belongs to exactly one.
  2. Each galaxy is a single connected piece — you can walk between any two of its cells without leaving it.
  3. 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.
  4. 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.

Questions and technique