How to play sudoku

The rules in one minute

A sudoku is a 9×9 grid divided into nine 3×3 boxes. Some cells already contain digits, called givens or clues. Your job is to fill every empty cell with a digit from 1 to 9 so that:

• every row contains each digit 1–9 exactly once,
• every column contains each digit 1–9 exactly once, and
• every 3×3 box contains each digit 1–9 exactly once.

That is the whole game. The givens cannot be changed, there is no arithmetic, and a proper sudoku has exactly one solution, so it can always be finished by logic, without guessing. Rows, columns and boxes are together called units; there are 27 of them, and each holds nine cells.

Words you will see

Cell

One of the 81 squares. We name cells by row and column: r3c5 is row 3, column 5.

Box

One of the nine 3×3 blocks, numbered 1–9 left to right, top to bottom.

Given

A digit printed at the start. Givens are shown in bold and cannot be edited.

Peers

The 20 other cells that share a row, column or box with a cell. A cell can never hold a digit that one of its peers holds.

Candidates (pencil marks, notes)

The digits that are still possible in a cell. Writing them down helps with harder puzzles.

How to play on NineByNine

1. Select a cell by tapping or clicking it, or move with the arrow keys.
2. Enter a digit with the number pad or your keyboard. Press Delete or Backspace (or the Erase button) to clear it.
3. Switch on Notes (or press N) to write candidates instead of answers. “Auto-notes” fills in every candidate for you.
4. Undo and redo work for every move. The Hint button gives three levels of help: the technique to use, where to look, and finally the move itself.
5. When the last digit is correct, you see your time, mistakes and hints, plus a spoiler-free result you can share.

Your progress is saved in your browser automatically, so you can close the tab and come back. Nothing is sent to a server.

Solving your first puzzle, step by step

Here is a real easy puzzle from our bank (code 1). The steps below are the first moves our solver finds, written out in the same words the hint button uses. Every one is a single: a cell that can take only one digit, or a digit that has only one place in a row, column or box.

1. Hidden single: 5 can only go in r2c5 in box 2.
2. Hidden single: 3 can only go in r3c7 in box 3.
3. Hidden single: 8 can only go in r2c8 in box 3.
4. Hidden single: 6 can only go in r2c7 in box 3.
5. Hidden single: 9 can only go in r1c9 in box 3.
6. Hidden single: 9 can only go in r3c3 in box 1.

Take the first step: Hidden single: 5 can only go in r2c5 in box 2. To check it yourself, look at the r2c5: every other empty cell there already sees that digit in its row, column or box. Place it, then look for the next one. On an easy puzzle you never need more than these two kinds of move. Play easy puzzles or play this exact puzzle.

Two ways to look at the grid

Ask where a digit can go. Pick a digit, say 5, and look at a box that has no 5 yet. Every 5 already placed rules out its entire row and column. If only one empty cell in the box survives, the 5 goes there. This is a hidden single, and it is the move that starts nearly every puzzle.

Ask what a cell can hold. Pick an empty cell and list the digits in its row, column and box. If eight different digits appear, the missing ninth is the answer. This is a naked single, and it becomes common as the grid fills up.

Alternate between the two. Each new digit you place can unlock several more, so after every placement, check the row, column and box you just changed.

When you get stuck

On medium and harder puzzles there will be moments where no single is available. That is the time for pencil marks. Write the candidates for a few crowded units and look for patterns: two cells that can only hold the same two digits (a naked pair), two digits that can only go in the same two cells (a hidden pair), or a digit confined to one line inside a box (a pointing pair). Each pattern removes candidates, which creates new singles. The strategies guide covers them in order.

A few habits help at every level:

• Work from the most crowded rows, columns and boxes first; they have the fewest possibilities.
• Do not guess. If you are not sure, leave the cell empty or write notes. A guessed digit that turns out wrong can be hard to untangle later.
• Keep notes current. When you place a digit, remove it from the notes of its peers (the “Auto-remove notes” setting does this for you).
• Use the highlights: selecting a cell shades its row, column and box, and selecting a digit shows every copy of it.
• If a puzzle feels impossible, use one level-1 hint. It names the technique without giving away the move.

How difficulty works here

Every puzzle is graded by the hardest technique our solver needs. Easy puzzles need only singles. Medium adds pointing pairs, box/line reduction and pairs. Hard adds triples, the X-Wing and the XY-Wing, and expert adds the Swordfish, Jellyfish, XYZ-Wing, unique rectangles and coloring. No puzzle ever needs trial and error. The number of givens matters less than you might expect: a puzzle with few givens can still be easy if the singles keep coming.

A short history of sudoku

Despite the Japanese name, the puzzle first appeared in the United States. In 1979 the American puzzle publisher Dell printed it under the name “Number Place”, as The Observer reported in 2005; the puzzles are usually credited to the puzzle constructor Howard Garns.

In 1984 the Japanese publisher Nikoli introduced the puzzle in Japan under the name “Suuji wa dokushin ni kagiru” (roughly, “the digits must be single”), which was later shortened to Sudoku. Nikoli notes that “Sudoku” is its registered trademark in Japan.

The worldwide boom started in Britain. Wayne Gould, a recently retired Hong Kong judge who had developed a computer program to produce puzzles, persuaded The Times to publish them; the paper launched its sudoku on 12 November 2004, other British newspapers soon followed, and the puzzle spread around the world from there.

Mathematicians took an interest too. A completed grid can be turned into a puzzle with surprisingly few givens, and for years nobody knew the minimum. In 2012, Gary McGuire, Bastian Tugemann and Gilles Civario announced an exhaustive computer search showing that no sudoku with 16 givens has a unique solution, so 17 is the minimum; the result was published in Experimental Mathematics in 2014.