# The mathematics of Septoku

• Published in 2008
In the collections
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.

## Other information

pages
11

### BibTeX entry

@article{Bell2008,
abstract = {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.},
author = {Bell, George I.},
month = {jan},
pages = 11,
title = {The mathematics of Septoku},
url = {http://arxiv.org/abs/0801.3697 http://arxiv.org/pdf/0801.3697v4},
year = 2008,
archivePrefix = {arXiv},
eprint = {0801.3697},
primaryClass = {math.CO},
urldate = {2013-12-22},
collections = {Puzzles,Easily explained}
}