# The mathematics of Septoku

- Published in 2008
- Added on

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.

## Links

## 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} }