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Sudoku Guide

How to play Sudoku

Sudoku is a logic puzzle where you fill empty cells with the numbers 1 through 9. Each row, each column, and each 3x3 box cannot contain the same number twice. Treat given numbers as clues, reduce candidates in each empty cell, and you can reach the solution step by step.

Sudoku puzzle
5
3
7
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1
9
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9
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8
6
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7
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Solved Sudoku
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Candidates

Write possible numbers lightly in each empty cell

You do not need to choose the answer immediately. Write the numbers that can fit in each empty cell, then remove numbers already present in the same row, column, or 3x3 box. As solving progresses, erase impossible candidates and confirm a value when only one candidate remains in a cell or one place remains in a unit.

Example notes for 8 and 9The upper-left 3x3 box already contains 1 through 7. The two remaining cells can only be 8 or 9, so write 8 and 9 as candidates in both cells instead of choosing immediately.
1
2
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5
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7

Beginner technique

Naked Single

Naked Single fixes a cell when only one candidate remains possible.

Naked Single applies when row, column, and 3x3 box restrictions remove every candidate from one cell except a single number. Since a number cannot repeat in the same row, column, or box, visible clues block candidates one by one. If only one number is left, that cell is fixed.

Cell with only candidate 4 leftThe center cell cannot use 1,2,3,5,6,7,8,9 because those numbers already appear in the same row, column, or box. Only candidate 4 remains, so the cell is fixed as 4.
5
6
7
8
1
2
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4
9

Beginner technique

Hidden Single

Hidden Single fixes a number when only one cell in a row, column, or box can contain it.

Hidden Single appears when a number can go in only one cell within a row, column, or 3x3 box. That cell may still show other candidates, but the unit must contain that number once. If there is no other place for it, that cell is fixed.

Hidden 7 in a boxIn the upper-left box, only the center cell can contain 7. The surrounding 7s block its row and column, so this cell is fixed as 7.
7
7
7
7
7

Intermediate technique

Naked Pair/Triple

Naked Pair/Triple removes candidates when matching candidate sets reserve two or three cells.

Naked Pair appears when two cells in the same row, column, or 3x3 box contain only the same two candidates. Those two numbers must occupy those two cells in some order, so the same candidates can be removed from other cells in that unit. Triple follows the same idea with three cells and three candidates.

Pair of 2 and 8The two yellow cells in the first row contain only candidates 2 and 8. Therefore 2 and 8 can be removed from the candidate cell on the right in the same row.
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9

Intermediate technique

Hidden Pair

Hidden Pair reserves two cells when two numbers can appear only in those same cells.

Hidden Pair appears when two numbers can appear only in the same two cells within one row, column, or 3x3 box. Those two cells are reserved for those numbers, so any other candidates mixed into those cells can be removed.

Hidden pair 2 and 3In column 2, candidates 2 and 3 appear only in the two yellow cells. Those cells must share 2 and 3, so other candidates in those cells are removed.
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6
9
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7
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3

Intermediate technique

Pointing Pair/Triple

Pointing Pair/Triple removes candidates outside a box when all matching box candidates sit on one line.

Pointing Pair/Triple applies when all candidates for a number inside one 3x3 box sit on the same row or column. The box must contain that number once, and if all possible places are on one line, the answer is on that line. The same candidate can then be removed from cells outside the box on that row or column.

Box candidate 6 gathered in one columnIn the center box, candidate 6 appears only in cells on column c4. Therefore candidate 6 is removed from the upper cell in the same c4 column outside the box.
9
1
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1
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2
1
1
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9
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8

Intermediate technique

Box-Line Reduction

Box-Line Reduction removes candidates inside a box when a row or column candidate is trapped there.

Box-Line Reduction applies when all possible cells for a candidate in a row or column are trapped inside one 3x3 box. That row or column must contain the number, and because the answer is inside that box, the same candidate can be removed from other rows or columns inside the box.

Row candidate 5 trapped in the center boxCandidate 5 in row 4 appears only inside the center box. Candidate 5 can therefore be removed from cells in the same center box that are not on row 4.
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2

Advanced technique

X-Wing

X-Wing removes candidates when one candidate forms four corners across two rows and two columns.

X-Wing appears when candidates for the same number form four corners across two rows and two columns. If two rows contain the candidate only in the same two columns, each row must place the number in one of those columns. Either way, those columns receive the number, so the same candidate can be removed from other cells in the columns.

X-Wing for candidate 3Candidate 3 appears in rows r2 and r4 only at columns c2 and c6, forming a rectangle. Other candidate 3s in the blue columns conflict with the pattern and are removed.
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8
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Advanced technique

Swordfish

Swordfish removes candidates when one candidate is locked across three rows and three columns.

Swordfish extends X-Wing to three lines. If a candidate repeats across three rows only within the same three columns, the three rows must place that number once in those columns. The columns are then locked by the pattern, so the same candidate is removed from other cells in those columns.

Swordfish for candidate 3Candidate 3 in rows r3, r4, and r8 appears only in columns c3, c6, and c9. This locks the three columns, so candidate 3 is removed from r3c4, r4c8, and r8c8.
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Advanced technique

XY-Wing

XY-Wing removes a shared candidate seen by two linked wing cells.

XY-Wing uses a pivot cell with two candidates and two wing cells. If the pivot is X,Y and the wings are X,Z and Y,Z, then one wing must become Z no matter which value the pivot takes. Any cell that sees both wings cannot contain Z. Here "sees" means sharing a row, column, or 3x3 box.

XY-Wing centered on 1 and 2The pivot r5c5 has candidates 1 and 2, while the wings r5c2 and r2c5 contain 1,9 and 2,9. Cell r2c2 sees both wings, so common candidate 9 is removed.
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