1 of 2
Which digit is missing from this row?
Level 1 · The basics
How to play classic sudoku
Every variant starts from the classic rules. Learn them cold and every variant is just an extra rule on top.
A sudoku grid has 81 cells in nine rows, nine columns and nine 3x3 boxes. Fill every cell so that each row, column and box holds the digits 1 to 9 exactly once. The starting digits are fixed, and a well-made puzzle has one solution.
Every variant on this site builds on these rules. When a puzzle says "normal sudoku rules apply," all of this still holds, and the variant adds one more rule on top.
How setters write it
The same rule, worded the ways you’ll see it on puzzles.
- Normal sudoku rules apply.
- Place the digits 1 to 9 once each in every row, column and 3×3 box.
- Classic sudoku rules apply.
Worth memorizing
- Each row, column and box holds 1 to 9 exactly once.
- When a variant’s rules begin with “normal sudoku rules apply”, everything here still holds.
- A digit that can go in only one place in a row, column or box goes there. This is the most common move in any puzzle.
Solving tips
Look for hidden singles
Pick a digit and a box, then check where that digit can still go. If a 7 in the row above and a 7 in the column beside cross off all but one cell, the 7 goes in that cell.
Find naked singles
Some cells can hold only one digit. If a cell's row, column and box already contain 1, 2, 3, 4, 5, 6, 8 and 9 between them, the cell must be 7.
Scan one digit at a time
Go through 1 to 9 and check every box for each digit. Each given digit rules out its whole row and column, so this is faster than studying cells one by one.
Use pairs to clear cells
If two cells in a row can each only be 3 or 8, those two cells take the 3 and the 8 between them. No other cell in that row can be 3 or 8, even before you know which cell is which.
A worked example: a naked pair in one row
We name cells by row and column, so row 1, column 2 is r1c2. Row 1 reads 1, blank, 4, blank, 6, blank, 9, blank, 5, so it is missing 2, 3, 7 and 8. Elsewhere, columns 2 and 4 each hold a 3 and a 7, column 6 holds a 3, and the top-left box holds an 8 at r2c3.
- Start with r1c2. The row allows 2, 3, 7 and 8. Column 2 already has a 3 and a 7, so r1c2 is 2 or 8. The same check on column 4 gives r1c4 the same two options, 2 or 8.
- Now r1c2 and r1c4 form a naked pair. Between them they hold the 2 and the 8, in some order. No other cell in row 1 can be 2 or 8, so r1c6 and r1c8 are down to 3 or 7.
- Column 6 already has a 3, so r1c6 can't be 3. That makes r1c6 a 7. The last open digit in the row, 3, goes in r1c8.
- Go back to the pair. r1c2 sits in the top-left box, and that box already has an 8 at r2c3. So r1c2 is 2 and r1c4 is 8.
- The row now reads 1, 2, 4, 8, 6, 7, 9, 3, 5. A quick check: 1 + 2 + 4 + 8 + 6 + 7 + 9 + 3 + 5 = 45, the total of every full row.
Practice
2 of 2
Which digit completes this box?
Reference table
| Technique | What you see | What you can remove |
|---|---|---|
| Naked single | A cell with one candidate left | That digit from the cell's row, column and box |
| Hidden single | A digit with one possible cell in a row, column or box | Every other candidate in that cell |
| Naked pair | Two cells in one house with the same two candidates | Those two digits from the rest of the house |
| Hidden pair | Two digits that fit only in the same two cells of a house | Every other candidate in those two cells |
| Naked triple | Three cells in one house whose candidates use only three digits | Those three digits from the rest of the house |
| Pointing | A digit's spots in a box all lie in one row or column | That digit from the rest of that row or column |
| Box-line reduction | A digit's spots in a row or column all lie in one box | That digit from the rest of that box |
Going deeper
Houses and where they overlap
Solvers call any row, column or box a house. Every classic technique is a statement about one house, or about the cells where a box meets a row or column. Each box shares three cells with three rows and three columns, and most intermediate moves live in those small overlaps.
Thinking in houses keeps your scanning honest. A hidden single can show up in a row even when the digit has three spots left in its box. Check all three kinds of house for each digit before you move on.
Pointing and box-line reduction
Say every spot for a 6 in the middle box lies in row 5. The box's 6 must be in row 5, so no other cell in row 5 can be 6, even in the boxes to the left and right. Solvers call this pointing.
The reverse also works. If every spot for a 6 in row 5 lies inside the middle box, then the box's 6 is in row 5. Cross 6 off the other two rows of that box. This move is called box-line reduction, or claiming.
Hidden pairs and triples
A naked pair is easy to spot because the notes match. A hidden pair sits among other notes. If 4 and 6 can each go only in the same two cells of a column, those two cells hold the 4 and the 6. Erase every other note in them.
Triples follow the same logic with three cells and three digits. A naked triple doesn't need every cell to show all three digits. Cells showing 12, 23 and 13 still form a triple, since those three cells use only three digits between them.
A good order for a stuck grid is simple. Scan for hidden singles one digit at a time, then naked singles, then pairs, then pointing. Go back to singles after every new digit, since one placement often opens up several more.
Common mistakes
Guessing when stuck
A well-made puzzle never needs a guess. If you're stuck, a logical move is waiting. Update your notes and rescan each digit from 1 to 9 across every row, column and box before you try anything else.
Leaving old notes in place
When you place a digit, erase it from the notes of every cell in its row, column and box. A stale note makes a cell look like it has two options when it has one, and it can hide a pair.
Scanning only the boxes
Hidden singles appear in rows and columns too. A digit may have three spots in its box and only one spot in its row. Scan rows and columns as often as boxes.
In mixed-rule puzzles
Classic rules are the base for every variant on this site. Most variant puzzles give few starting digits, so the extra rule creates the first placements and the classic moves finish the job. Pairs, pointing and hidden singles still work in any variant, and they often combine with the new rule. A killer cage can create a pair, and that pair then clears its row in the classic way. When a puzzle mixes two variant rules, return to classic scanning after each new digit.
Questions solvers ask
What are the rules of sudoku?
Place the digits 1 to 9 in each row, column and 3x3 box so that no digit repeats in any of them. The starting digits can't be changed.
Do you need math to solve sudoku?
No. Classic sudoku uses digits only as symbols, so there is no adding. Variants such as killer and arrow sudoku do use sums.
What is a hidden single in sudoku?
A hidden single is a digit that has only one possible cell left in a row, column or box. A naked single is a cell that has only one possible digit left.
Can a sudoku have more than one solution?
A well-made puzzle has exactly one solution, and you can reach it by logic without guessing. Puzzles with two or more solutions are considered broken.
How do you solve sudoku when you get stuck?
Update every note first. Then scan each digit from 1 to 9 across all rows, columns and boxes for hidden singles. If that finds nothing, look for pairs and pointing. A missed hidden single is the usual cause.
What is a naked pair in sudoku?
Two cells in the same row, column or box that can each only be the same two digits. Those two digits belong to the pair, so remove them from every other cell in that row, column or box.
What is the fewest clues a sudoku can have?
A classic 9x9 sudoku with one solution needs at least 17 starting digits. Variant puzzles can need far fewer, because their extra rules carry the information.
Sudoku Variants Series (001) - Odd Sudoku
Sudoku Variants Series (000) - Classic Sudoku
Zig Zag: Classic
White Diamond: Classic