Galaxies

In a Galaxies puzzle, you are given a grid with dots placed on it, including dots inside cells and on grid lines. The goal is to divide the grid into connected regions such that each region contains exactly one dot and every region has rotational symmetry around its dot. You solve it by drawing boundaries around each dot's territory, working from cells whose ownership is forced by the symmetry constraint.

The puzzle is published by the Japanese publisher Nikoli, known for popularizing other logic puzzles like Sudoku and Kakuro. The name Tentai Show (天体ショー) translates roughly to 'astronomical show,' reflecting the rotational symmetry of the regions which resemble galaxies rotating around a central point. The puzzle is also widely known in English as Galaxies for the same reason.

In a Galaxies puzzle, every region must be identical when rotated 180 degrees around its dot. This means that for every cell on one side of the dot, there must be a corresponding cell on the opposite side at the same distance. Dots placed on edges or corners of cells create different symmetry conditions, which is the key to deducing boundaries.

Yes, Galaxies puzzles appear in Nikoli's printed puzzle books and have been adapted by several puzzle websites and apps, including Simon Tatham's Portable Puzzle Collection under the name 'Galaxies.' The puzzle type has also appeared in puzzle competitions. Difficulty varies with grid size and dot placement, with larger grids requiring more advanced deduction techniques.