On this page
Sudoku is a logic puzzle about where digits can go.
In classic Sudoku, you start with a 9×9 grid containing a set of fixed clues. Your job is to fill the remaining cells so that every row, every column, and every 3×3 box contains the digits 1–9 exactly once.
The digits are labels, not calculations. Solving comes from using the grid's restrictions to rule out impossible positions until placements or eliminations are logically forced.
- Row
- Column
- Box
- Target cell
What is the goal of Sudoku?
The goal of Sudoku is to complete every empty cell while satisfying the row, column, and box constraints at the same time.
For a classic 9×9 Sudoku, a completed grid must satisfy three conditions:
- Every row contains the digits 1–9 exactly once.
- Every column contains the digits 1–9 exactly once.
- Every 3×3 box contains the digits 1–9 exactly once.
The digits printed in the starting puzzle are called givens or clues. They stay fixed. The remaining cells are solved from those clues and from the restrictions created by every digit you add.
The objective is therefore not simply to fill all 81 cells. It is to fill them in a way that satisfies all three overlapping constraints everywhere in the grid.
How does Sudoku work?
Sudoku works because every unsolved cell belongs to one row, one column, and one box. Each of those units restricts which digits are allowed in that cell.
Starting clues
A Sudoku begins with some cells already filled. Those givens create the initial structure of the puzzle.
A properly constructed classic Sudoku is expected to lead to one solution from the supplied clues. The clues do not tell you directly what every empty cell contains; they create enough restrictions for a chain of deductions to be possible.
Rows, columns, and boxes
Every placed digit affects three units at once. If a 5 already appears in a cell's row, column, or box, that cell cannot also contain 5.
The overlap between these units is what makes Sudoku interesting. A digit that is still possible from the perspective of a row may be impossible because of the box. A position that looks ambiguous inside one box may become forced once you consider an intersecting column.
Solving by elimination
Most Sudoku logic can be understood as elimination.
You begin with the digits 1–9 as theoretical possibilities for an empty cell, then rule out digits that conflict with the row, column, or box. If only one possibility remains, the cell is solved. In harder puzzles, several cells may retain multiple possibilities, and solving techniques help you prove additional eliminations before the next placement becomes available.
That basic cycle — restrict possibilities, make a deduction, update the grid, repeat — remains the same from beginner puzzles to advanced ones.
Is Sudoku a math puzzle?
Sudoku uses digits, but solving a standard Sudoku does not require arithmetic.
If a row already contains 1, 2, 3, 4, 5, 6, 7, and 9, you do not need to calculate anything to find the missing digit. You know that 8 is the only member of 1–9 that is absent.
The same would be true if the puzzle used nine distinct symbols instead of the digits 1–9. The numerical values are convenient labels. They do not need to be added, multiplied, or arranged into equations.
There is mathematics behind Sudoku as a combinatorial object, and some variants add arithmetic constraints, but playing classic Sudoku is primarily a logic and pattern-recognition task.
Why is Sudoku a logic puzzle?
A logical Sudoku move has a reason that follows from the current grid.
Suppose you are considering whether an empty cell could contain 7. If its row already contains 7, then 7 is impossible there. The same is true if the 7 appears in its column or box. If all other digits can also be eliminated, 7 becomes a forced placement.
More advanced techniques do not change the rules. They organize the same restrictions into larger patterns. A pair may prove that two candidates are reserved for two cells. An X-Wing may prove that a candidate must occupy one of two positions in each of two rows. A chain may combine several implications. In every case, the conclusion is supposed to be justified by the grid rather than chosen because it “looks right.”
What are clues, candidates, and solved cells?
Three terms appear constantly in Sudoku explanations:
- Clue / given: a digit supplied by the puzzle at the start. It is fixed.
- Solved cell: an originally empty cell whose digit has been logically determined and entered.
- Candidate: a digit that can still legally fit in an unsolved cell based on the information currently available.
Candidates are possibilities, not answers. A cell containing candidates {2, 7} is not telling you to choose between 2 and 7. It is telling you that the current grid has ruled out the other seven digits and that more information is still required.
When only one candidate remains in a cell, you have a Naked Single. When one digit has only one possible cell within a row, column, or box, you have a Hidden Single.
Does Sudoku always use a 9×9 grid?
No, but 9×9 is the standard form usually meant by classic Sudoku.
The classic grid has 81 cells arranged into nine rows, nine columns, and nine 3×3 boxes. Smaller formats such as 4×4 or 6×6 can use the same general idea with different region sizes, while larger Sudokus extend the symbol set and grid.
There are also Sudoku variants that keep a 9×9 grid but add extra constraints, such as diagonals, cages, irregular regions, or relationships between neighboring cells.
When a guide on VeyraPlay says classic Sudoku, it refers to the standard row, column, and 3×3 box rule set unless stated otherwise.
Does a Sudoku have only one solution?
A properly constructed classic Sudoku puzzle is expected to have a unique solution: one completed grid that satisfies all of its clues and constraints.
That is different from saying that uniqueness is a fourth row/column/box rule. The three structural constraints define what a valid completed grid looks like. Uniqueness is a property of the particular puzzle created by its starting clues.
It is possible to create a partially filled Sudoku grid with multiple valid completions. Puzzle construction and validation therefore need to check that the chosen set of clues determines exactly one solution.
Uniqueness also becomes relevant to some advanced solving techniques, but beginners do not need uniqueness-based reasoning to understand how Sudoku works.
Do you have to guess in Sudoku?
Not when the goal is logical solving.
You can always enter a speculative digit and see what happens, but that is trial and error rather than a deduction from the current state. A logical solve asks for a reason before making a placement or elimination.
Easy puzzles may need only direct scanning and Singles. Hard puzzles can require candidate patterns, links, coloring, or chains. Being stuck does not automatically mean the puzzle requires a guess; it may mean the next logical pattern is harder to recognize.
Some computer-solving methods deliberately explore possibilities by search or backtracking. That is useful for verification and generation, but it is a different question from how a human-oriented logic guide teaches the puzzle.
What does “Sudoku” mean?
The modern name Sudoku became associated with the puzzle through Japanese publisher Nikoli. The puzzle form had circulated earlier under names including Number Place.
The name is now used internationally for the puzzle family, but the history of Sudoku is broader than the name itself. The dedicated history guide covers the development of Number Place, Nikoli's role, and the puzzle's later worldwide popularity in more detail.
How do you start playing Sudoku?
A beginner does not need a large catalog of techniques.
Use this progression:
- Learn the three Sudoku rules.
- Understand how rows, columns, boxes, and cells overlap.
- Look for a row, column, or box with only one missing digit.
- Scan individual digits across the grid.
- Learn Naked Singles and Hidden Singles.
- Add candidates when direct placements become difficult to see.
- Move to intermediate eliminations only when the puzzle actually needs them.
The key habit is to place a digit because you can justify it, then re-check the affected row, column, and box for the next simple deduction.
FAQ
Do you need to be good at math to play Sudoku?
No. Standard Sudoku does not require arithmetic. You need to track which digits are allowed in each row, column, box, and cell.
What numbers are used in Sudoku?
Classic 9×9 Sudoku uses the digits 1 through 9. Their numerical values are not important; they function as nine distinct symbols.
Is Sudoku always solvable?
A correctly published puzzle should have a valid solution, but an arbitrary partially filled grid may be invalid, unsolvable, or have multiple solutions. Puzzle validation is what distinguishes a properly constructed Sudoku from an arbitrary set of clues.
What is the first Sudoku technique to learn?
Start with last-missing-digit placements, scanning, Naked Singles, and Hidden Singles. They teach the core idea of finding a forced position before you move into candidate eliminations.
What should I learn after the basic rules?
Learn how the grid works, then practice scanning, candidates, Naked Singles, and Hidden Singles before moving to Locked Candidates and subsets.
What to learn next
If this is your first Sudoku, continue with Sudoku Rules and How to Play Sudoku. If you already know the rules but want a systematic solving method, move to How to Solve Sudoku. For the vocabulary behind harder solving, continue with The Sudoku Grid and Sudoku Candidates.