How to Play Sudoku
Sudoku is the number puzzle you have seen on the back pages of the newspaper, next to the crossword. It looks like arithmetic, but it is not. You never add, subtract or multiply. The nine numbers could just as well be nine colors or nine letters. The whole puzzle is about one question: where can this number go?
This page teaches the game from the very beginning. If you have never filled in a single square, you are in the right place. Read it through once, then try an Easy puzzle. Most people have the hang of it within ten minutes.
The Grid
A Sudoku grid is a large square made of 81 small squares. It helps to know three words:
- Row: nine squares side by side, running left to right. There are 9 rows. We count them from the top, so row 1 is the top row.
- Column: nine squares stacked up and down. There are 9 columns. We count them from the left, so column 1 is the left edge.
- Box: a block of nine squares, three wide and three tall, marked off by thick lines. There are 9 boxes: top-left, top-middle, top-right, and so on down to bottom-right.
Every square belongs to exactly one row, one column and one box. The square in row 1, column 1, for example, is in the top row, the left-hand column and the top-left box.
When a puzzle starts, some squares already hold a number. These are the printed numbers, also called givens or clues. In our game they are shown in heavy black type. They are correct, and they never change. The empty squares are yours to fill.
The One Rule
Sudoku has a single rule, applied three ways:
Fill every empty square with a number from 1 to 9 so that each row, each column and each box holds every number from 1 to 9 exactly once.
Put another way, a number may never appear twice:
- in the same row,
- in the same column, or
- in the same box.
That is all. There is no rule about diagonals, no sums to check and nothing to count. A well-made puzzle has exactly one answer, and you can reach it by reasoning. You never need to guess, and in our game you never have to. Every puzzle is tested before you see it.
Your First Move: A Worked Example
The basic move in Sudoku is to pick one number and one box, and ask: where in this box can the number go? Here is the top-left box of a puzzle, along with what we know about the lines that cross it. We want to place a 7.
| Top-left box | Column 1 | Column 2 | Column 3 | What we know about the row |
|---|---|---|---|---|
| Row 1 | empty | 4 | empty | Row 1 has a 7 further right |
| Row 2 | empty | empty | 9 | No 7 in row 2 yet |
| Row 3 | 2 | empty | empty | Row 3 has a 7 further right |
We also know that column 1 already has a 7 lower down the grid. Now reason it through:
- The box has no 7 yet, so one of its six empty squares must take it.
- Row 1 already has a 7. That rules out both empty squares in row 1.
- Row 3 already has a 7. That rules out both empty squares in row 3.
- Two squares are left, both in row 2: column 1 and column 2.
- Column 1 already has a 7. That rules out the square in row 2, column 1.
- One square is left: row 2, column 2. The 7 goes there.
Notice that we never guessed. We crossed off squares until one was left. This is called finding the only place for a number, and it is enough to finish every Easy puzzle on this site. The new 7 then helps with the next step, because it rules out 7 for the rest of row 2 and the rest of column 2.
The Second Basic Move: The Only Number for a Square
You can also turn the question around. Instead of asking where a number can go, pick one empty square and ask which numbers can go here?
Say a square's row already holds 1, 2, 5 and 9, its column holds 3 and 6, and its box holds 4 and 8. Count them off: 1, 2, 3, 4, 5, 6, 8 and 9 are all taken. Only 7 is missing, so the square must be 7.
This move is at its easiest when a row, column or box has just one empty square left. Whatever number is missing goes in the gap.
How to Play on This Site
- Tap an empty square. It turns yellow, and its row, column and box are shaded so you can see which numbers are already used there.
- Tap a number on the number pad to write it in. Tap a different number to change it.
- Or pick the number first. With no square marked, tap a number and then tap each square where it goes. This is handy for filling in all the 5s in one pass. Tap the number again to stop. You can make this the usual way to play in Settings.
- Erase clears the marked square. Undo takes back your last step, and the one before that, as far back as you like.
- The number pad counts for you. Under each number it says how many are still missing, such as "3 left." When all nine are placed it says "Done."
- Matching numbers light up. Tap a square with a 6 in it and every 6 on the grid is shaded and underlined, which makes it easy to see where the next 6 can't go.
On a computer you can also use the keyboard: the arrow keys move around the grid, the number keys write a number, Backspace erases, and the N key switches notes on and off.
Notes: Your Pencil Marks
Sooner or later you will find a number that could go in two squares, and you can't yet tell which. Solvers on paper write the number small in the corner of both squares and move on. These small numbers are called notes, pencil marks or candidates.
In our game, tap Notes to switch it on. Now the numbers you tap are written small instead of large. A square can hold several notes at once. Tap the same number again to rub a note out. Tap Notes once more to go back to writing real answers.
Two things make notes easier here than on paper:
- When you place a real number, the matching notes in its row, column and box are rubbed out for you.
- Fill In Notes writes every number that is still possible into every empty square. It is a big help on Hard puzzles. On Easy puzzles you will rarely want notes at all.
Mistakes, Hints and Checking
Because each puzzle has exactly one answer, a number is either right or wrong. On Easy puzzles our game tells you straight away: a wrong number turns red, gets a wavy underline and a small cross in its corner. Take it back with Undo or Erase and try again. Nothing is lost and there is no score.
On Medium and Hard puzzles the marks start switched off, the way a newspaper puzzle works. You can turn them on or off for any level in Settings, under "Tell me right away when a number is wrong."
Hint never just blurts out an answer. It marks one square, shades the row, column or box that proves it, and tells you the reason in plain words, for example: "This is the only place for a 7 in row 4." It always chooses the simplest reason on the board. If a number you wrote earlier is wrong, the hint points to that first, since nothing else can be trusted until it is fixed.
The Three Levels
Our levels are graded by the kind of reasoning a puzzle needs, not only by how many numbers are printed.
| Level | Printed numbers | What it takes |
|---|---|---|
| Easy | About 36 to 40 | The two basic moves on this page. One square at a time, no notes needed. |
| Medium | About 28 to 30 | The basic moves, plus now and then a pair of squares or a number pinned to one line of a box. |
| Hard | About 22 to 27 | Notes, and patterns that reach across several rows or columns. Still never a guess. |
The methods for Medium and Hard are explained with examples in our Sudoku strategy guide.
Puzzle Numbers and the Daily Puzzle
Every puzzle has a number, shown above the grid, such as Puzzle #48213. The same number at the same level always gives the same puzzle. If you enjoyed one, tell a friend the number and the level, and they can type it into Settings and play the very same grid.
The Daily Puzzle button gives you the puzzle for today's date. There is one for each level, and it is the same for everybody, which makes it a nice thing to share over the phone or across the breakfast table.
Common Questions from Beginners
Do I need to be good at math?
No. There is no math in Sudoku. If you can tell whether a 5 is already in a row, you have every skill the puzzle asks for.
Where should I start?
Start with the number that is printed most often, or with the box, row or column that has the fewest gaps. Both give you the least to check.
What if I get stuck?
Change what you are looking at. If you have been working through boxes, scan the rows instead. If that fails, tap Hint. Reading why the hinted square works is the fastest way to learn.
How long does a puzzle take?
An Easy puzzle takes most people 10 to 20 minutes at first. There is no time limit, and the timer stays hidden unless you ask for it. Your puzzle is saved after every step, so you can stop and come back whenever you like.
If You Like Sudoku
Sudoku suits people who enjoy quiet, careful puzzles. If that is you, try Mahjong Solitaire, another calm puzzle with no clock, or FreeCell, a card game where nearly every deal can be won by planning. And when you are ready for more, our guide to Sudoku variations explains the other kinds of grid you may meet in puzzle books.