The mathematics of Septoku

• Published in 2008
• Added on 2013-12-22

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

• http://arxiv.org/abs/0801.3697
• http://arxiv.org/pdf/0801.3697v4

Other information

BibTeX entry

@article{Bell2008,
	key = {Bell2008},
	type = {article},
	title = {The mathematics of Septoku},
	author = {Bell, George I.},
	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.},
	comment = {},
	date_added = {2013-12-22},
	date_published = {2008-01-01},
	urls = {http://arxiv.org/abs/0801.3697,http://arxiv.org/pdf/0801.3697v4},
	collections = {Puzzles,Easily explained},
	month = {jan},
	pages = 11,
	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}
}