Constraints of Clue Geometry
It has been postulated that no proper sudoku can have clues limited to the range of positions in the pattern below.
The largest rectangular orthogonal "hole" (region with no clues) in a proper sudoku is believed to be a rectangle of 30 cells (a 5 x 6 rectangular area). One such example is the following with 22 clues:
The largest total number of empty groups (rows, columns, and squares) in a sudoku is believed to be nine. One example is the following; a sudoku which has 3 empty squares, 3 empty rows, and 3 empty columns and gives 22 clues.
Read more about this topic: Mathematics Of Sudoku
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