  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 given values is six. We
generalize the puzzle to other board shapes, and devise a puzzle on a
star-shaped board with 73 cells with six givens which has a unique solution. We
show how this puzzle relates to the unsolved Hadwiger-Nelson problem in
combinatorial geometry.
