9x9ruudukon

9x9ruudukon, or a nine-by-nine grid, is a square grid consisting of nine rows and nine columns, yielding 81 individual cells. It is widely used in puzzles and numerical games, most notably Sudoku. The grid is typically subdivided into nine 3x3 subgrids called boxes or regions, which are often delineated by a heavier border or shading.

In Sudoku, the objective is to fill the grid so that each row, each column, and each 3x3 box contains all digits from 1 to 9 exactly once. The grid thus functions as a constraint satisfaction problem. Solving methods rely on logical deduction, pattern recognition, and, in more difficult cases, exploratory backtracking. Common techniques include scanning for missing numbers, using candidate lists (pencil marks), and identifying patterns such as naked or hidden singles, pairs, and triples.

Coordinates are typically used to reference cells, with rows labeled A through I and columns labeled 1 through 9, or by (row, column) pairs. The nine 3x3 regions are formed by grouping rows in sets of three and columns in sets of three, producing a convenient framework for applying puzzle rules.

Beyond Sudoku, 9x9 grids appear in other puzzles and educational activities, such as Latin squares, magic square variants, or tasks for teaching grid coordinates, arithmetic, and logical reasoning. The uniform 9x9 structure provides a common foundation for a variety of puzzle types and learning activities.