How to Play Sudoku: Rules and First Moves

Sudoku is played on a 9×9 grid that is split into nine rows, nine columns and nine 3×3 boxes. A few cells start with digits in them. You fill every empty cell with a digit from 1 to 9, so that each row, each column and each box holds every digit exactly once. A proper puzzle has only one solution, and you reach it by logic, with no math and no guessing.

Everything below is shown on a real easy puzzle from this site: the parts of the grid, the rule in action, and the first digits you can place.

The grid and its parts

The grid has 81 small squares called cells. They form three kinds of group, and the rule treats all three the same way:

• A row runs across the grid. Rows are counted from the top, one to nine.
• A column runs down. Columns are counted from the left.
• A box is one of the nine 3×3 blocks marked off by the thicker lines. Box one is top left and box nine is bottom right.

Lessons on this site call any row, column or box a house, and name a cell by its row and column: row four, column three is the fourth cell down in the third column. The digits printed at the start are the givens. You cannot change them, and every deduction starts from them.

The one rule, with a worked example

The whole game is one rule: a digit may appear only once in each row, once in each column and once in each box. A house has nine cells and they must all hold different digits, so every digit from 1 to 9 ends up in each house exactly once.

That rule tells you what an empty cell cannot be. A cell sees every other cell in its row, its column and its box, and it cannot take any digit it sees. So the question to ask about an empty cell is this: which digits are missing from all three of its houses?

Take row four, column three in the example.

• Its row holds 1, 3 and 7.
• Its column holds 5, 6, 7 and 9.
• Its box holds 2, 5, 7 and 8.

Together those rule out eight digits: 1, 2, 3, 5, 6, 7, 8 and 9. Only 4 is left, so 4 goes in the cell. Some digits turn up in more than one list (7 is in all three), and that changes nothing. What counts is which digits the cell sees, not how many times. The lesson on the last possible number covers this move in full.

How to start a puzzle

Checking cells one at a time works, but it is slow on a fresh grid, where most cells still have several options. A faster way to start is to scan: pick one digit, then take one box and ask where that digit can still go.

Try the digit 1 in box four, the middle box on the left. Box four has no 1 yet and five empty cells.

• The 1 in row four, at column seven, rules out both empty cells of box four in that row.
• The 1 at the top of column one rules out both empty cells of box four in that column.

One empty cell is left, row six, column three, so the 1 goes there. As far as its own houses go, that cell could also hold a 3 or a 4. It makes no difference: box four needs a 1, and no other cell in the box can take it. This move is a hidden single.

The first singles

Both moves above are singles, places where only one answer is possible. They come in two views, and easy puzzles are made of little else.

• Cell view: a cell sees eight different digits, so only one digit can go there. This one is called the last possible number.
• Digit view: a digit has only one cell left in a row, column or box. This one is called the hidden single.

Once you keep pencil marks, the small notes of the digits a cell could still take, the cell view gets a third name: a cell left with one mark is a naked single. The pencil marks lesson shows how to keep them.

A routine for a new puzzle

Scan the digits 1 to 9 one at a time across all nine boxes and place every single you find. After each placement, check the row, column and box of the new digit again, because it may have just left another cell with one option. When a full pass finds nothing, start pencil marks.

Hard puzzles start the same way. Of the 3,341 puzzles on this site, from easy to extreme, all but five open with a single. What changes at the higher levels is what you need once the singles run out.

Common beginner mistakes

• Guessing. A wrong guess can sit unnoticed for many moves and only show up as a clash near the end, when it is hard to trace back. If no single is left, start pencil marks or ask for a hint instead.
• Forgetting the box. A digit that fits its row and its column can still clash with a copy in its box. Check all three houses every time.
• Placing a digit because it fits. Fitting is not enough. A digit is forced only when it is the one option for its cell, or the cell is the one place left for it in a house.
• Notes that go out of date. When you place a digit, every cell that sees it loses that digit as an option. The game on this site removes it from those cells' notes for you. On paper you have to do it yourself.
• Starting too hard. Almost every easy puzzle here can be finished with singles alone (480 of 484), which makes them the right place to get quick at scanning. Move up a level when the scan feels routine.
• Treating it as math. The digits are only labels. Nothing is added up, and the puzzle would work the same with nine letters or nine colors.

Difficulty levels on this site

There are six levels, plus a daily puzzle. Each puzzle's level comes from its Sudoku Explainer rating, which is set by the hardest step in its solve. Here is what the 3,341 puzzles on the site need, level by level:

• Easy: 30 starting digits. Singles alone are enough for all but four of the 484.
• Medium: 21 to 23 starting digits for nearly all. About two in three finish with singles. The rest need one step more, such as a pointing pair or a naked pair.
• Hard: 21 to 23 starting digits for nearly all, yet none finishes with singles. The hardest step is a wing, a uniqueness pattern such as the unique rectangle, a subset, or a fish such as the X-wing.
• Expert: mostly a chain on one digit, such as the X-chain.
• Master and extreme: forcing chains that move between digits and cells, with an occasional Nishio.
• Daily: a new puzzle every day.

So past easy, the number of givens barely changes: 2,833 of the 2,857 puzzles above easy start with 21 to 23. A hard puzzle is hard because of the techniques it needs. It starts with about as many digits as a medium one.

Where to go next

• The learning path puts the techniques in solving order, starting with how to read the grid.
• The techniques guide has every lesson, grouped by chapter.
• The solver takes a puzzle you type, paste or carry over from a game, and works through it one step at a time, naming the technique behind each move.
• Easy puzzles are where to try the scan for real, and the daily puzzle gives you a fresh grid each day.

Sudoku FAQ

How do you play sudoku?

You fill a 9×9 grid with the digits 1 to 9 so that no digit repeats in any row, column or 3×3 box. Some digits are given at the start, and you work out the rest from them, one cell at a time.

What are the rules of sudoku?

There is one rule, applied to three kinds of group: each row, each column and each 3×3 box must contain the digits 1 to 9 once each. Nothing else is required. The puzzle is solved when all 81 cells are filled and no group repeats a digit.

How does sudoku work?

Every given rules out its own digit for the other cells in its row, column and box. Put enough of those together and some cell is left with one option, or some digit with one place. Each digit you place rules out more options, so the puzzle opens up as you go.

What is the best way for a beginner to solve sudoku?

Scan one digit at a time: for each box, check where that digit can still go, and place it when only one cell is left. Then look for cells that see eight different digits. Almost every easy puzzle here needs nothing more than these two moves, so start there.

Do you ever have to guess in sudoku?

No. A proper sudoku has exactly one solution, and logic alone can reach it. Getting stuck means the puzzle needs a technique you have not learned yet. The techniques guide lists them in the order you will meet them.