Sudoku Techniques Guide
This guide introduces solving techniques from naked singles to pairs and triples, following this app's five difficulty levels one rung at a time.
On this page
The rules in 30 seconds
Sudoku has exactly one rule: no digit may appear twice in any row, any column, or any box outlined in bold. On a 9×9 board, the digits 1 to 9 each appear exactly once per row, column, and box. The digits filled in from the start (the givens) are fixed.
Smaller boards play by the same rule. A 6×6 fills 1 to 6 into 2×3 boxes, and a 4×4 fills 1 to 4 into 2×2 boxes. With fewer cells to scan, the small boards work well for a child's first sudoku or for practicing techniques.
Starting habits: scanning and notes
Start with the fullest rows, columns, and boxes. In a row with eight cells filled, the empty cell is already decided, and a unit with seven filled leaves only two candidates. Every cell you fill narrows the neighboring units in turn, so the crowded spots are the fastest way in.
When you start getting stuck, turn on Notes (the pencil) and jot down which digits could go in each empty cell. Notes in this app aren't filled in automatically. You toggle them yourself, and working out the candidates on your own is what builds skill.
Learn to scan the other way around too. Pick one digit (say, 5), find every 5 on the board, and check where a 5 can still go in each box. The hidden singles introduced below fall straight out of this scan.
Naked Singles — Starter
Look at an empty cell and cross off every digit already present in its row, column, and box. If exactly one digit survives, that cell is settled. You only need to look at that one cell, which makes this the most basic technique.
Starter puzzles are built so you can solve them all the way through with naked singles alone. Use them to get a feel for which cell to look at next, and build up speed on the small 4×4 and 6×6 boards.
Worked example: three cells, one possible digit each
Try this 9×9 Starter puzzle. We will fill three cells without guessing or an answer sheet, using only the digits already in their row, column, and box. One new digit helps unlock other cells.
Rows are numbered from top to bottom, columns from left to right. Each thick-bordered box contains 3×3 cells.
| Row and column numbers | Column 1 | Column 2 | Column 3 | Column 4 | Column 5 | Column 6 | Column 7 | Column 8 | Column 9 |
|---|---|---|---|---|---|---|---|---|---|
| Row 1 | 3 | 2 | 6 | Empty | 1 | Empty | 8 | Empty | Empty |
| Row 2 | 4 | 8 | 1 | 9 | Empty | 5 | 7 | Empty | Empty |
| Row 3 | Empty | Empty | Empty | 8 | 2 | 6 | 4 | 1 | Empty |
| Row 4 | Empty | Empty | Empty | Empty | Empty | Empty | 3 | 8 | Empty |
| Row 5 | 7 | Empty | Empty | 1 | Empty | 9 | Empty | Empty | 6 |
| Row 6 | Empty | 5 | 2 | Empty | Empty | Empty | Empty | Empty | Empty |
| Row 7 | Empty | 6 | 5 | 3 | 4 | 1 | Empty | Empty | Empty |
| Row 8 | Empty | Empty | 8 | 2 | Empty | 7 | 6 | 5 | 4 |
| Row 9 | Empty | Empty | 4 | Empty | 6 | Empty | 9 | 3 | 1 |
Show the three moves and their explanations
Underlined digits are the ones we added. The outlined cell is the one filled in the current step. All other digits were there at the start.
Step 1: row 1, column 6
Start at row 1, column 6. List the digits missing from its row, then cross off anything already present in its column or box.
- Row 1 is missing 4, 5, 7, 9. These are our starting candidates.
- Column 6 already contains 5, 7, 9. Cross those off. Remaining candidates: 4.
- The same 3×3 box does not contain 4, so that remaining digit is allowed.
Only 4 fits. Fill row 1, column 6 with 4.
| Row and column numbers | Column 1 | Column 2 | Column 3 | Column 4 | Column 5 | Column 6 | Column 7 | Column 8 | Column 9 |
|---|---|---|---|---|---|---|---|---|---|
| Row 1 | 3 | 2 | 6 | Empty | 1 | 4 Added in the walkthrough | 8 | Empty | Empty |
| Row 2 | 4 | 8 | 1 | 9 | Empty | 5 | 7 | Empty | Empty |
| Row 3 | Empty | Empty | Empty | 8 | 2 | 6 | 4 | 1 | Empty |
| Row 4 | Empty | Empty | Empty | Empty | Empty | Empty | 3 | 8 | Empty |
| Row 5 | 7 | Empty | Empty | 1 | Empty | 9 | Empty | Empty | 6 |
| Row 6 | Empty | 5 | 2 | Empty | Empty | Empty | Empty | Empty | Empty |
| Row 7 | Empty | 6 | 5 | 3 | 4 | 1 | Empty | Empty | Empty |
| Row 8 | Empty | Empty | 8 | 2 | Empty | 7 | 6 | 5 | 4 |
| Row 9 | Empty | Empty | 4 | Empty | 6 | Empty | 9 | 3 | 1 |
Step 2: row 1, column 4
Keep the 4 from step 1. Row 1 now has only three missing digits. For this cell, checking the row and column is not enough: the box makes the final decision.
- Row 1 is missing 5, 7, 9. These are our starting candidates.
- Column 4 already contains 9. Cross those off. Remaining candidates: 5, 7.
- The same 3×3 box already contains 5. Cross those off too; only 7 remains.
Only 7 fits. Fill row 1, column 4 with 7.
| Row and column numbers | Column 1 | Column 2 | Column 3 | Column 4 | Column 5 | Column 6 | Column 7 | Column 8 | Column 9 |
|---|---|---|---|---|---|---|---|---|---|
| Row 1 | 3 | 2 | 6 | 7 Added in the walkthrough | 1 | 4 Added in the walkthrough | 8 | Empty | Empty |
| Row 2 | 4 | 8 | 1 | 9 | Empty | 5 | 7 | Empty | Empty |
| Row 3 | Empty | Empty | Empty | 8 | 2 | 6 | 4 | 1 | Empty |
| Row 4 | Empty | Empty | Empty | Empty | Empty | Empty | 3 | 8 | Empty |
| Row 5 | 7 | Empty | Empty | 1 | Empty | 9 | Empty | Empty | 6 |
| Row 6 | Empty | 5 | 2 | Empty | Empty | Empty | Empty | Empty | Empty |
| Row 7 | Empty | 6 | 5 | 3 | 4 | 1 | Empty | Empty | Empty |
| Row 8 | Empty | Empty | 8 | 2 | Empty | 7 | 6 | 5 | 4 |
| Row 9 | Empty | Empty | 4 | Empty | 6 | Empty | 9 | 3 | 1 |
Step 3: row 4, column 6
Follow column 6 down to row 4. Before step 1 this cell could hold 2 or 4. The new 4 in the same column rules out 4 here.
- Row 4 is missing 1, 2, 4, 5, 6, 7, 9. These are our starting candidates.
- Column 6 already contains 1, 4, 5, 6, 7, 9. Cross those off. Remaining candidates: 2.
- The same 3×3 box does not contain 2, so that remaining digit is allowed.
Only 2 fits. Fill row 4, column 6 with 2.
| Row and column numbers | Column 1 | Column 2 | Column 3 | Column 4 | Column 5 | Column 6 | Column 7 | Column 8 | Column 9 |
|---|---|---|---|---|---|---|---|---|---|
| Row 1 | 3 | 2 | 6 | 7 Added in the walkthrough | 1 | 4 Added in the walkthrough | 8 | Empty | Empty |
| Row 2 | 4 | 8 | 1 | 9 | Empty | 5 | 7 | Empty | Empty |
| Row 3 | Empty | Empty | Empty | 8 | 2 | 6 | 4 | 1 | Empty |
| Row 4 | Empty | Empty | Empty | Empty | Empty | 2 Added in the walkthrough | 3 | 8 | Empty |
| Row 5 | 7 | Empty | Empty | 1 | Empty | 9 | Empty | Empty | 6 |
| Row 6 | Empty | 5 | 2 | Empty | Empty | Empty | Empty | Empty | Empty |
| Row 7 | Empty | 6 | 5 | 3 | 4 | 1 | Empty | Empty | Empty |
| Row 8 | Empty | Empty | 8 | 2 | Empty | 7 | 6 | 5 | 4 |
| Row 9 | Empty | Empty | 4 | Empty | 6 | Empty | 9 | 3 | 1 |
Each move is a naked single: checking the row, column, and box leaves one candidate. Continue with the same habit on the other empty cells. The play link opens this same puzzle; it does not apply these three moves for you.
Solve this puzzleLocked Candidates — Medium
If all of a digit's candidate cells within one box fall on the same row (or column), the digit must land in that row of that box, so you can erase it as a candidate from that row's cells outside the box. The same logic works in reverse, narrowing a box from a row or column.
This technique erases notes without filling any cell directly. Medium puzzles center on a chain: erased notes give rise to fresh naked and hidden singles. This is where a habit of tidy note-keeping starts to pay off.
Pairs and Triples — Hard
Naked Pair: if two cells in a unit hold exactly the same two candidates, those two digits must go in those two cells, so you can erase both digits as candidates from the unit's other cells.
Hidden Pair: if two digits can only go in the same two cells of a unit, those cells belong to those digits, so you can erase every other candidate written in them. Extend the Naked Pair idea to three cells and three digits and you have a Naked Triple.
Hard puzzles are graded to be solvable by adding pairs and triples on top of singles and locked candidates. These techniques are invisible without notes, so from this level on, notes are no longer optional.
Expert — beyond the ladder
Expert boards can't be finished with the techniques above alone. The single-solution guarantee still holds, though, so you can always reach the answer with higher-level techniques or with careful reasoning, such as assuming one of the two remaining candidates in a cell and hunting for a contradiction.
A hint can help you move forward when you are stuck. It tries the app's logical techniques first, but may fill a cell from the solution when those techniques cannot provide a usable move. It does not explain an advanced technique, so examine the candidates yourself if you want to practice the reasoning.
Practicing with this app
This app's difficulty levels work as a curriculum. During generation, a real grader checks whether the puzzle can be solved completely using only the techniques up to each level, so climbing from Starter upward teaches you the techniques above one at a time.
Hints first look for a logical move on the current board and check it against the solution. If no usable move is found, a hint fills or corrects a cell from the solution. Show conflicts only flags duplicate digits in a row, column, or box. Hint use and conflict checking are recorded alongside your ranking result.
If you're playing with kids, learn the rules on the 4×4, which uses only the digits 1 to 4, then move up through 6×6 to the classic 9×9. With A4 printing, several small boards fit on one sheet, which is useful for worksheets.