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Squarematch - Marshall Squares™


I came across Marshall Squares™ on the Kadon Gamepuzzles website in January, 2007.

These are made with 5 colors, with at most 2 sharing a tile equally, and there are 25 of them.

An obvious arrangement of them is into a 5x5 square, with the edges matching. That is quite difficult, as there are only 16 different ways to do it (not counting rotations, reflections, and color swaps).

See them HERE.

If we move the corner squares to centers of the edges, as in the figure at the right, the task is much easier. Then there are nearly fifteen hundred times as many ways to fit the 25 squares together -- 23558 to be exact.

Here is a sample of them:

the first one has the 'butterfly' or 'argyle' pieces clustered in 3 groups.
the second one has four of the solids in the extremities and each color forms a continuous path through the figure.


These two are rotated 45° to show their striking symmetry.