The mathematics of Septoku

Details The mathematics of Septoku The mathematics of Septoku

2008-01-24

arxiv.org/abs/0801.3697v3

Mathematics

Combinatorics

10 pages, 9 figures; completely rewritten, results no longer rely on an integer programming model

Scientific paper

Septoku is a Sudoku variant invented by Bruce Oberg, played on a hexagonal grid of 37 cells. We show that up to rotations, reflections, and symbol permutations, there are only six valid Septoku boards. In order to have a unique solution, we show that the minimum number of starting seeds or clues is six. We generalize the puzzle to other board shapes, and devise a 6-seed puzzle on a star-shaped board with 73 cells that has a unique solution. We show how this puzzle relates to the unsolved Hadwiger-Nelson problem in combinatorial geometry.

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