Over this past holiday season, I learned about Tantrix which is a game or puzzle involving hexagonal tiles. Tantrix can be enjoyed as a multi-player game or as a solo Tantrix puzzle. I was introduced to a Tantrix puzzle involving 10 tiles. I took a picture of the tiles along with a picture of the tile backs for reference. As the tile backs indicate, the puzzle is to form a closed loop of a given color for 3 through 10 tiles. All touching tile edges must match in color.
I manually solved up to 7 tiles, pretty much by trial and error without trying to formulate an algorithm or method. I decided it would be more interesting to write software to solve this Tantrix puzzle.
The software took a couple of days to write. It displays the connected hexagons with color edges shown. From there, I assembled the solution into a more meaningful display with tile graphics. The solutions are not necessarily unique - the software stops after finding the first solution.
3 tiles yellow
4 tiles red
5 tiles red
6 tiles blue
7 tiles red
8 tiles blue
9 tiles yellow
10 tiles blue
Depending on whose rules one goes by, it could be challenged that this is not a solution because of the unused cell position in the middle, but I rather like it.
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