How to Solve Sudoku
To solve a sudoku, fill the grid so every row, column and 3×3 box has the digits 1 to 9 once. Start by finding cells where only one digit fits and digits that fit in only one cell. When that stops working, write candidates and use patterns such as pairs, pointing pairs and X-Wings.
The rules
A sudoku is a 9×9 grid divided into nine 3×3 boxes. Some cells already have a digit. You fill the rest so that every row, every column and every box contains each of the digits 1 to 9 exactly once. You never need to add numbers up; the digits are only labels.
Step by step
- Read the rule: each row, column and 3×3 box holds 1 to 9 exactly once.
- Scan for hidden singles: pick a digit and find the one cell in a box where it fits.
- Look for naked singles: a cell where only one digit is still possible.
- When stuck, write candidates in the empty cells.
- Use pairs and pointing pairs to remove candidates, then look for new singles.
- For hard puzzles, look for triples and X-Wings.
1. Singles: the base of every puzzle
Hidden single. Pick a digit, say 5. Look at a box where 5 is missing. Every row and column that already has a 5 rules out the cells in that line. If only one cell is left in the box, the 5 goes there. The same works for rows and columns.Naked single. Look at one empty cell and list which digits already appear in its row, column and box. If eight of the nine are used, the last one is the answer. Easy puzzles on this site can be solved with these two techniques alone.2. Candidates
When singles run out, write the possible digits, called candidates, in small print in each empty cell. Do it one box at a time and double-check: a missing candidate leads to mistakes later. Every time you place a digit, erase it from the candidates in its row, column and box.
3. Pairs and pointing pairs (medium)
- Naked pair: two cells in the same unit both have only the candidates 3 and 7. One is 3 and the other is 7, so no other cell in that unit can be 3 or 7.
- Hidden pair: digits 2 and 8 can only go in the same two cells of a unit. Those cells must be 2 and 8, so remove their other candidates.
- Pointing pair: in a box, digit 4 can only go in two cells, both in the same row. The 4 for that row must be inside this box, so remove 4 from the rest of the row.
- Box/line reduction: in a row, digit 6 only fits in cells of one box. Remove 6 from the other cells of that box.
4. Triples and the X-Wing (hard)
- Naked triple: three cells in a unit whose candidates together are only three digits, such as {1,4}, {4,9} and {1,9}. Those digits are used up there and can be removed from the rest of the unit.
- Hidden triple: three digits that only fit in the same three cells of a unit. Remove all other candidates from those cells.
- X-Wing: digit 7 has exactly two places in row 2 and two in row 6, and they are in the same two columns. The 7s must sit on opposite corners, so remove 7 from the rest of those two columns.
5. Swordfish, XY-Wing and chains (expert)
The swordfish extends the X-Wing to three rows and three columns. The XY-Wing uses three cells with two candidates each: whatever the middle cell becomes, one of the outer cells must take the shared digit, so that digit can be removed where both outer cells can see. Beyond that, players use chains: "if this cell is 3, then that cell is 8, then…". These are the techniques expert puzzles need.
Common mistakes
- Placing a digit because it "looks right" without checking the column. Always check row, column and box.
- Forgetting to erase a candidate after placing a digit.
- Writing digits in pen. Pencil and an eraser make every level more fun.
- Guessing. With one solution, there is always a logical next step, even if it is hard to see.
Levels on this site
| Level | Given numbers | Median | Techniques needed |
|---|---|---|---|
| Easy | 36–40 | 38 | Naked and hidden singles only |
| Medium | 30–35 | 31 | Singles plus naked or hidden pairs, pointing pairs and box/line reduction |
| Hard | 26–31 | 28 | All of the above plus naked or hidden triples or an X-Wing |
| Expert | 24–28 | 28 | Swordfish or XY-Wing, or longer chains that go beyond the techniques the grader knows |
Given numbers measured on 1000 generated puzzles per level (October 15, 2026). The level comes from which techniques a step-by-step solver needs, not from the count of given numbers.
Frequently asked questions
What are the rules of sudoku?
Fill the 9×9 grid so that each row, each column and each of the nine 3×3 boxes contains the digits 1 to 9 exactly once. Some digits are given at the start. A proper puzzle has one solution.
What is the best way to start a sudoku?
Scan for hidden singles. Take the digit that appears most often, then check each box where it is missing: often it fits in only one cell. Repeat with the next digit. This finds many numbers quickly.
Should I write candidates?
For easy puzzles you usually do not need to. For medium and harder puzzles, candidates are how you find pairs, triples and X-Wings. Write small digits in the corners of the cells, in pencil.
Is sudoku a math game?
No arithmetic is needed. The digits are just nine different symbols; letters or colors would work the same. Sudoku is a logic puzzle about placing each symbol once in every row, column and box.
Who invented sudoku?
The modern puzzle was first published in the United States in 1979 by Dell Magazines under the name Number Place. The Japanese publisher Nikoli made it popular in Japan in the 1980s and gave it the name sudoku.
How many sudoku grids are there?
There are 6,670,903,752,021,072,936,960 different completed 9×9 sudoku grids, as calculated by Bertram Felgenhauer and Frazer Jarvis in 2005. That is why a generator never runs out of new puzzles.
Last updated: October 15, 2026