The mathematics of Septoku
Combinatorics
2020-03-16 v5 Discrete Mathematics
General Mathematics
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.
Keywords
Cite
@article{arxiv.0801.3697,
title = {The mathematics of Septoku},
author = {George I. Bell},
journal= {arXiv preprint arXiv:0801.3697},
year = {2020}
}
Comments
11 pages, 9 figures; added two recent references