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Spiral Galaxies

The universe is big, and contains many galaxies. Unlike popular belief, these galaxies completely cover the universe, and there are no big empty spaces. How are the galaxies distributed over the universe?

Partition the universe into spiral galaxies, in such a way that the galaxies together cover the whole universe, and each individual galaxy is rotation symmetric over 180 degrees around a given spiral.

Example

As an example, we will divide a universe of sixteen squares into five spiral galaxies. We know that every square belongs to one of the galaxies, so let us start with the square in the top left. This square belongs to one of the spirals, and if it belongs to a given spiral, then also the square opposite of this one must belong to the same spiral. For four of the spirals this square would be outside the universe, only the leftmost spiral is feasible.

In the same way, we see that the bottom left square must belong to the spiral directly to the right of it, and that the two empty squares at the right border of the universe must belong to the most central spiral. Now, when we also include the opposite squares of those four, we know for every square in the universe which spiral it belongs to, and we can fill in the borders.

Background

Spiral Galaxies was invented by Nikoli. The Japanese name is Tentai Show.


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