The solution to colouring the square can be found by firstly colouring in a diagonal, and looking at the limited choices from there.

So, for instance, colour the diagonal from top left to bottom right. You now have two choices for the two other corners - select one (it doesn't matter which - they are mirror images of one another). Now you only have one choice for the middle of the left column, or for the middle of the bottom row (depends upon your selection). You can now fill in the other diagonal, and you're home and dry.

The solution is:

We can convert this by shearing into a diamond shape:

Rows stay as rows. Columns become angled, but the cells are still in a line. One diagonal is still in existent, but there is no second diagonal.

So any solution to the square problem is a solution to the diamond (but not necessarily vice versa).

Chopping off cells, we end up with a solution to the hexagon problem:

Here is another solution:

Are these the only two solutions to this puzzle? I don't know - if you find out, please tell me....

page date: 27Oct05.      I enjoy correspondence stimulated by this site. You can contact me here.