It was time to put up the Christmas tree at the polyomino house. The tree formed the outline shown below, and was made from the 12 pentominoes and 5 tetrominoes. It was decorated with 12 unit-square baubles which were hung in a symmetric pattern. The baubles were not allowed to touch each other or the edge of the tree - not even at the corners. They were pleased with the arrangement shown until someone pointed out that it could be made in 120 different ways (or 240 including reflections). So the search began for symmetric bauble positions which had unique solutions, apart from reflections.
I found four such solutions. George Sicherman sent solutions for another four, making a total of eight.
Hover over the image to see a solution.
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Tree pattern with 120 solutions, not counting reflections. Re-arrange the unit-square baubles to find unique symmetric arrangements. |