How to play Sudoku

This page solves the first seven cells of a real Easy puzzle from this site, with the reasoning for each, so you can see what “only one digit can go” looks like on an actual board.

What is the goal?

A classic Sudoku is a 9×9 grid divided into nine boxes of 3×3 cells. Some cells start with a digit, called a given. Your job is to fill in the rest so that no digit repeats in any row, column or box. Every puzzle on this site has exactly one solution, so you never need to guess. If you can’t see the next move, the puzzle contains a deduction you haven’t found yet. The rules page is the reference for the exact wording and for the variants, and this page is about how to think while solving.

The puzzle we will solve

The puzzle below is the second one in the site’s Easy pool for classic Sudoku, and it starts with 29 givens, so 52 cells are empty. The row and column numbers are along the edges. In this guide a cell is written as r3c7, which means row 3, column 7, counting rows from the top and columns from the left. The 81-character string for the puzzle is 46....2...53.14..77....6.39.....7.9.8....2.5.53..6......5.4..71.4..8.9...9.....4., with a dot for each empty cell.

Take a minute to look at it before reading on. Notice that the givens are not spread evenly. Some digits, such as 4 and 9, appear several times, and a digit that appears many times has the fewest places left to go. That is where to start.

First habit: ask where a digit can go in a row, column or box

Pick a digit and a row, and ask: in this row, which empty cells could hold this digit? A cell can hold it only if the digit doesn’t already appear in that cell’s column or box. If just one cell survives, the digit must go there. This is a hidden single, and it is the technique most beginners rediscover on their own. The hidden singles lesson covers it in more depth.

Move 1: the 4 in row 3 goes in r3c7. Row 3 has five empty cells: columns 2, 3, 4, 5 and 7. Check each for a 4. Column 2 already has a 4 at r8c2, and box 1 has one at r1c1, so r3c2 is out. Box 1 also rules out r3c3. A 4 at r2c6 rules out r3c4 (it shares box 2) and r3c5 as well. Only r3c7 is open, so it is a 4.

Move 2: the 9 in column 1 goes in r2c1. Column 1 has five empty cells: rows 2, 4, 7, 8 and 9. A 9 at r4c8 sits in row 4. A 9 at r9c2 sits in row 9 and in box 7, which also covers rows 7 and 8 of column 1. A 9 at r8c7 sits in row 8. That removes rows 4, 7, 8 and 9, leaving r2c1.

Move 3: the 2 in row 2 goes in r2c4. After move 2, row 2 has three empty cells, in columns 4, 7 and 8. The 2 at r1c7 sits in column 7 and also in box 3, which removes both r2c7 and r2c8. Only r2c4 is left.

Second habit: ask what a single cell can hold

The other habit starts from a cell and asks which digits are still possible. Look at every digit in that cell’s row, column and box. Whatever is missing from the combined list is a candidate. If only one digit is missing, that is the answer. This is a naked single, and the naked singles lesson goes deeper.

Move 4: r3c5 is 5. Row 3 now holds 7, 6, 4, 3 and 9. Column 5 holds 1, 6, 4 and 8. Box 2 holds 2, 1, 4 and 6. Together these cover 1, 2, 3, 4, 6, 7, 8 and 9. The only digit not on the list is 5.

Move 5: r3c4 is 8. With the 5 in place, the digits seen from r3c4 across its row, column and box are 1, 2, 3, 4, 5, 6, 7 and 9. The missing digit is 8.

Moves 6 and 7 work the same way: r4c5 can only be 3, and r5c5 can only be 9. Writing these in made the middle of column 5 almost complete, which is typical. A filled cell narrows down every neighbor it can see.

What the board looks like after seven moves

The digits you have just placed are in bold.

Row 3 has only two empty cells left, and column 5 has only two. Several cells that had many possibilities at the start now have only one or two. You do not have to find the best move each time. Any valid single is progress, and the order does not change the final answer.

Why rescanning matters: move 5 depends on move 4

The order of the moves above is not arbitrary, and one pair shows why. Before move 4, the cell r3c4 could still hold either a 5 or an 8. Both digits were missing from its row, column and box, so nothing forced a choice. Once move 4 put a 5 in r3c5, which is in the same row and the same box, the 5 was no longer possible in r3c4, and the 8 was the only digit left. The cell itself had not changed. A neighbor had been filled, and that was enough.

This is the reason to rescan after each placement and to start with the cells the new digit touches. A digit you place in a row, a column and a box affects up to twenty other cells. A beginner who scans the whole board again from the top-left corner each time will find the same moves eventually, but the neighbors of the last digit are where new moves most often appear.

Where to start scanning

There is no single correct starting point, but a few habits reduce the search.

• Start with digits that appear often. A digit with many copies already on the board has few legal places left, so each row, column and box has fewer cells to check for it. In this puzzle the 4 appears five times among the givens and the 9 four times, so they are good first choices.
• Start with crowded houses. A row, column or box with many givens has few empty cells, so each empty cell has fewer possible digits. Row 3 started with four givens and five empty cells, and its 4 was settled by the first move.
• Work one digit at a time through all nine boxes. Take a digit, look at where it already sits, and see which boxes can still take it only in one place. This is the same hidden single question, asked box by box.
• Cross off as you go. If you keep a mental or written list of which digits a row still needs, naked singles are easy to see when only one digit is missing.

The pencil marks guide explains how to write candidates in the cells when scanning in your head becomes too much. On Easy puzzles most players don’t need them.

The loop that solves an Easy puzzle

1. Scan. Look for a digit that fits in only one cell of some row, column or box, or a cell that can hold only one digit.
2. Place. Write the digit in.
3. Rescan. The new digit changes the rows, columns and boxes it touches, so look at those first.
4. Repeat until the grid is full or you can’t find a move.

The site’s own solver does exactly this. It tries naked singles first and hidden singles second, and for this puzzle those two techniques are all it needs: it fills all 52 empty cells with 38 naked singles and 14 hidden singles and never guesses. The split between the two depends on which technique the solver tries first. A person scanning for digits would probably find more hidden singles. Easy puzzles on this site are defined as ones that need nothing else, as described in how difficulty is graded.

What if you get stuck?

Check the basics first. Go back over each row, column and box and ask whether you missed a digit. Most stalls on an Easy puzzle come from a missed single, not a missing technique. Look at the digits that appear most often on the board and see where their last copy can go. If you have carefully re-scanned and there really is nothing, the puzzle is above Easy. Use a hint, which names the technique, or read the pencil marks guide, because writing small candidates in the cells makes harder patterns visible.

If you place a wrong digit, the contradiction will usually surface a few moves later, when some cell has no legal digit left or a digit has no cell. The game’s mistake setting can flag conflicts as you go, and the controls page lists the settings and keys.

Where to go next

• Play an Easy puzzle on the home page and try to finish it using only the two habits above.
• When Easy feels comfortable, move on to Medium. The strategy guide for each difficulty says what to learn first, and the techniques hub has a lesson for every technique in order.
• For a complete system for harder puzzles, read how to solve Sudoku.
• Browse the guides hub for other tutorials.