Sudoku (originally called Number Place) is a logic-based, combinatorial number-placement puzzle. In classic Sudoku, the objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 subgrids that compose the grid (also called “boxes”, “blocks”, or “regions”) contain all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, which for a well-posed puzzle has a single solution.

Game Interface

Overview & History

Howard Garns, a 74-year-old retired architect and freelance puzzle constructor from Connersville, Indiana, most likely designed the modern Sudoku anonymously. Dell Magazines first published it in 1979 as Number Place. The puzzle became popular in Japan in 1986 under the name Sudoku (meaning “single number”) and gained international popularity in 2005.

Mathematics of Sudoku refers to the study of Sudoku puzzles using combinatorial mathematics. Valid Sudoku grids are a specific type of Latin square. The formula below shows the number of valid 9×9 Sudoku solution grids:

This immense number of possibilities ensures that random generation can produce effectively unique puzzles for every session. Students often use Sudoku to practice logical deduction, specifically “reductio ad absurdum” (proof by contradiction), where the player tentatively places a number to see if it leads to an impossible state.

Game Mechanics

The standard Sudoku grid is a specific case of a constraint satisfaction problem. Three main rules define the constraints:

• Row Constraint: Every row must contain digits 1 through 9 exactly once.
• Column Constraint: Every column must contain digits 1 through 9 exactly once.
• Box Constraint: Every 3×3 region must contain digits 1 through 9 exactly once.

The complexity of the techniques required to solve the puzzle determines its difficulty, rather than the number of given digits. Computer algorithms, such as the backtracking algorithm used in this tool, solve Sudoku by systematically trying numbers and backtracking when a dead end is reached.

Frequently Asked Questions

What is the minimum number of clues required?

Mathematicians have proven that a valid Sudoku puzzle with a unique solution must have at least 17 starting clues. Puzzles with 16 or fewer clues either have multiple solutions or no solution.

Does this tool offer hints?

This utility provides visual assistance rather than direct hints. It highlights the row, column, and box of the selected cell to aid in scanning. The “Check Mistakes” function acts as a verification step, identifying logical contradictions based on the current board state.

Is guessing required to solve Sudoku?

Most published puzzles do not require guessing. Players can solve them using pure logic. However, extremely advanced “diabolical” puzzles may require a technique called “bifurcation” (trying a path to see if it fails), which mimics a guess.

See Also