Magic Stars of David

There are 80 unique magic stars, excluding reflections and rotations. These can be arranged as a basic set of 20, where each one of these 20 can be transformed into 3 further stars eg by swapping the cells with the same colour here (eg swap the 2 red cells, the 2 yellow cells, etc):

This transformation can be repeated on the other 2 axes at 120 degrees to the one shown, giving us a total set of 4 stars.

You can easily see why this works: the top row of coloured cells all end up swapped with the bottom row, so both these rows are still magic; each diagonal row only experiences a change of position of the same cells - eg the 2 red cells still stay on the same row - and thus stay magic.

Here is a a text file with all 80 magic stars (left click to view, right click to save).

See also Magic Hexagrams

page date: 18Mar04.      I enjoy correspondence stimulated by this site. You can contact me here.