How to solve sudoku, step by step

Sudoku is played on a grid of 9 rows and 9 columns, split into nine 3×3 boxes. Some cells already contain a digit. Your job is to fill every empty cell with a digit from 1 to 9 so that the grid is complete and correct. You never need to guess, because each step follows from the steps before it.

This guide explains the rules, the words used to describe the grid, and the two techniques that solve every Easy puzzle. If you want to see how the later techniques build on these ideas, the Learn hub lists them in order.

The three rules

Every sudoku follows the same three rules:

• Rows. Each of the nine rows must contain the digits 1 to 9, each exactly once.
• Columns. Each of the nine columns must contain the digits 1 to 9, each exactly once.
• Boxes. Each of the nine 3×3 boxes must contain the digits 1 to 9, each exactly once.

That is the whole game. Every technique in this series is a clever way of applying these three rules.

Words that make the rest easier

Sudoku writing uses a few words again and again:

• Given. A digit that was in the puzzle when you started. Givens never change.
• Cell. One square of the grid. In this series, cells are named by row and column: r3c5 means row 3, column 5. Rows are numbered 1 to 9 from the top, and columns 1 to 9 from the left.
• Unit. A row, a column or a box. Each unit must contain every digit once.
• Candidate. A digit that is still possible in an empty cell. Pencil marks, or notes in Hush, are your list of candidates for each cell.

Naked singles: the cell with one option

What is a naked single?

A naked single is an empty cell that has only one candidate left. The other eight digits have been ruled out by the filled cells in its row, column and box, so the one remaining digit must go there.

How it works

Pick an empty cell and cross out every digit that already appears in its row, its column or its box. If only one digit is left, write it in. That is the whole technique.

In this picture, the cell marked ? sees the digits 1 to 8 in its row. Only 9 is left, so the cell must be 9. To keep the picture simple, only the row is shown. In a real puzzle you would check the column and the box too, and those extra digits often produce a naked single sooner.

How to spot it

• Look at nearly full units. A row, column or box with six or seven digits already in it leaves only two or three empty cells, and each one has fewer candidates.
• Check after every placement. A new digit removes a candidate from every cell in its row, column and box. Look at those cells again, because one of them may now have a single candidate.
• Scan the empty cells. Ask of each one: how many digits does it still need?

Hidden singles: the digit with one place

What is a hidden single?

A hidden single is a digit that has only one possible cell in a row, column or box. That cell may still show several candidates, but the digit can go nowhere else in the unit, so it must go in that cell.

How it works

Choose a unit and a digit that is missing from it. For each empty cell in the unit, ask whether the same digit already appears in that cell’s row, column or box. If it does, the digit is blocked there. When only one empty cell is not blocked, the digit goes in that cell.

The cells marked - are the ones where the 6 is ruled out. Each one sees a 6. The cells in r4c1 and r4c2 and r4c3 share box 4 with the 6 in r5c1, and r4c1 also shares column 1 with it. The cells r4c4, r4c5 and r4c6 share box 5 with the 6 in r6c5, and r4c5 also shares column 5 with it. Only r4c7 is left, so the 6 must go there.

How to spot it

• Pick a missing digit. Choose a digit that does not yet appear in the unit, then check where it can go.
• Look for blocking digits. Each copy of that digit in a neighboring row, column or box blocks a few cells. The more blocked cells, the fewer places are left.
• Use the highlights. Hush highlights matching numbers, so you can see every copy of a digit at once.

A worked example

Look again at row 4 in the picture above. The digits 1 and 2 are already in the row, so the 6 must go in one of the seven empty cells. Check them in turn.

• r4c1 is in column 1, which already has a 6 in r5c1. Ruled out.
• r4c2 and r4c3 are in box 4, which also holds that 6. Ruled out.
• r4c4, r4c5 and r4c6 are in box 5, which holds the 6 in r6c5. Ruled out.
• r4c7 is in column 7 and box 6. Neither contains a 6, so it stays open.

Place the 6 in r4c7. That placement then removes 6 from the rest of column 7 and from box 6, which may reveal new singles.

Common mistakes

• Checking only the row and column. Many beginners forget the box. A digit in the same box blocks a cell just as a digit in the row does.
• Confusing candidates with singles. A cell with three candidates is not a single. Wait until only one candidate is left, or until a digit has only one place in a unit.
• Forgetting to re-check. One placement can unlock several singles in a row. Scan the affected units again before you move on.

A simple routine for every move

1. Start with a digit that already appears many times on the board. It is usually easiest to place.
2. Look for naked singles across the grid.
3. Choose a unit and look for hidden singles in it.
4. After each placement, re-check the row, column and box it went into.
5. When no singles remain, add notes to the empty cells and look for the techniques in the next guides.

When you get stuck

Stuck players often try to solve the whole grid at once. Work on one unit at a time instead. If that still fails, add notes: list the candidates for every empty cell. Hush’s notes clean themselves up when you place a number, so your candidate lists stay accurate. The “fill in all notes” tool adds every candidate in one step.

If you cannot see the next move, take a break. Hush can be paused at any time and the game is always saved. The timer pauses when you leave the app, so a short break does not cost you anything.

Practice these techniques in Hush

Easy puzzles in Hush use only naked singles and hidden singles, which are the techniques on this page. Easy and Medium are unlimited and free, and the daily puzzle is free every day. Once singles feel natural, the next step is locked candidates, the first Medium technique. For playing habits that help while you learn, read sudoku tips for beginners. If you prefer to play without interruptions, Sudoku without ads explains how Hush is designed, and offline sudoku explains how every puzzle ships with the app. After locked candidates, the next step is naked pairs. You can see the whole app on the Hush home page.