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• An empty board is fully determined by a single value, it's "order", which for a 9x9 board is 3.
• The board is viewable in terms of rows, columns and blocks.
  • Each row, column and block has exactly order2 cells, e.g. for order = 3, each row, column and block has 9 cells.
  • Each board has exactly order2 rows, columns and blocks.
• Each cell is a member of exactly one row, one column and one block.
  • No rows share the same cell.   Likewise, no columns or blocks share cells.  This forces the square matrix layout  of rows, columns, and order^2 sub-matrix of blocks if one were to display the rows, columns and blocks where each cell is only shown once.
• The rules of Sudoku stipluate that the value in any given cell has very specific constraints:

  • Wiki Markup
    The valid values are {{1...order*order}}^{{2}}^ (inclusive), e.g. for order=2, the allowed values are \[1, 2, 3, 4\]

  •  Any valid value in a cell cannot appear in another cell in the row, column or block to which that cell belongs.   Conversely, each row, column or block must contain every valid value exactly once.

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