{
  "id": "0801.3697",
  "version": "v5",
  "published": "2008-01-24T16:04:22.000Z",
  "updated": "2020-03-12T22:48:56.000Z",
  "title": "The mathematics of Septoku",
  "authors": [
    "George I. Bell"
  ],
  "comment": "11 pages, 9 figures; added two recent references",
  "categories": [
    "math.CO",
    "cs.DM",
    "math.GM"
  ],
  "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.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-12-16T04:54:01.000Z",
      "comment": "11 pages, 9 figures; many minor changes",
      "journal": null,
      "doi": null
    },
    {
      "version": "v5",
      "updated": "2020-03-12T22:48:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "00A08",
      "97A20"
    ],
    "keywords": [
      "mathematics",
      "unique solution",
      "valid septoku boards",
      "puzzle relates",
      "bruce oberg"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.3697B"
    }
  }
}