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The Sudoku Game

Sudoku is a 9*9 9x9 grid-based puzzle in which the goal is to place numbers from 1 to 9 in the grid squares taking into account specific constraints. The 9 x 9 * 9 puzzle grid can be seen as divided into 9 sub-grids of size 3*33x3. The 3 main conditions in the classic version of Sudoku state are that each square in the grid contains a number from 1 to 9 and a number cannot be repeated:

• In any line
• In any column
• In any on the 3*3 3x3 sub-puzzles

 Sudoku Sudoku is not limited to 9x9 boards.  An "order" for a Sudoku puzzle can be defined, and thus a Sudoku puzzle is an order2 x order2}} matrix.    A regular Sudoku puzzle is this order = 3.   The above rules can be generalized to any order.   This is Rice, so our system should be able to handle any order of Sudoku puzzle.

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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 order*order cells, e.g. for order = 3, each row, column and block has 9 cells.
  • Each board has exactly order*order rows order^2^ 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 orderxorder 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}} (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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