How to Solve a Sudoku: A Step-by-Step Beginner Walkthrough

If you have never played, the one rule is this: fill the grid so that every row, every column and every 3×3 box holds the digits 1 to 9 exactly once. Our how to play page covers it in more detail. Everything below uses only that rule.

How to name a square

Rows are numbered 1 to 9 from top to bottom, columns 1 to 9 from left to right, and boxes 1 to 9 reading like a book (box 1 is top left, box 3 top right, box 9 bottom right). "Row 2, column 5" is the fifth square along in the second row.

The puzzle

This is an easy puzzle from the same generator that makes the puzzles on our easy page. It starts with 38 digits and has exactly one solution. Every digit can be found with one idea: a square where only one digit is still possible. (That idea is called a naked single.)

Before writing anything, look at where the grid is crowded. Row 8 already has seven digits. Row 2 has six. Box 3, at the top right, has only three, but part of row 2 runs through it, so it will open up once row 2 is done. Crowded places leave few choices, so that is where to start.

Step 1: finish the busiest row

Row 8 reads _ 9 3 1 7 _ 4 8 6. Only 2 and 5 are missing, in column 1 and column 6.

Which goes where? Look at the box around row 8, column 1: box 7, bottom left. It already holds a 5 (in row 9). So column 1 cannot be the 5, and must be the 2. That leaves the 5 for column 6.

Notice what happened. We did not try a digit and see if it worked. We ruled one out, and the other was forced. That is the whole method, repeated about 40 times.

Step 2: row 2, three gaps

Row 2 reads 3 5 1 _ _ 7 _ 6 2. The missing digits are 4, 8 and 9, and the gaps are in columns 4, 5 and 7.

• Column 5 already contains an 8 (row 9) and a 9 (row 7). The only one of the three that fits is 4.
• Now 8 and 9 are left for columns 4 and 7. Column 7 already has an 8 (row 6), so column 7 gets the 9.
• Column 4 takes the last digit, 8.

Five digits placed, and the grid now looks like this. The newest digits are shaded.

Step 3: box 3, from the box's point of view

Rows can run out of easy gaps, so switch to boxes. Box 3 now holds 1, 2, 6 and 9 (the 9 is the one we just placed). It is missing 3, 4, 5, 7 and 8, in five squares. Take each square in turn and cross off what its row and column already contain.

• Row 3, column 7. Row 3 contains 3 and 7, so those are out. Column 7 contains 4 and 8, so those are out. Only 5 is left.
• Row 3, column 8. The box is now missing 3, 4, 7 and 8. Row 3 rules out 3 and 7; column 8 contains an 8. That leaves 4.
• Row 1, column 8. Missing in the box: 3, 7 and 8. Column 8 has a 3 (row 9) and an 8 (row 8). So this square is 7.
• Row 1, column 7. Two left, 3 and 8. Column 7 has an 8, so this one is 3.
• Row 3, column 9 takes the last digit in the box, 8.

Box 3 is full. Ten digits in, and we have used nothing but crossing off.

Step 4: keep the chain going

Every digit you place is new information for its row, column and box. The 3 we put in row 1, column 7, for example, now blocks 3 from the rest of row 1. The quickest way to keep moving is to look next at the places your last digits touched:

1. Row 1 is now 3, 7, 1 on the right and 2 in column 3. Its remaining squares have fewer options than before.
2. Row 3 gained three digits in one go. Check each of its gaps.
3. Column 7 and column 8 are filling up too.

Try it yourself. In row 3, column 1, the row now holds 1, 3, 4, 5, 7 and 8. Box 1 adds a 2, and column 1 has a 6 (row 9). What is left? Only 9. Then row 3, column 3 has just 2 and 6 left from the row, and box 1 already has a 2. So it is 6.

When nothing jumps out: scan by digit

Sometimes no square looks obvious. Then turn the question around. Instead of asking "what goes in this square?", ask "where does this digit go?"

Pick a digit, say 7, and find a box with no 7 yet. Every 7 already in the grid blocks its whole row and column. Shade those rows and columns in your head. If only one square in the box is left unblocked, the 7 goes there.

That method is called a hidden single. You do not need it for this puzzle, but it is the first thing medium puzzles ask of you, and it is often faster than checking squares one by one.

The finished grid

Carry on the same way and every square falls in turn. Here is the full solution, so you can check your work. Shaded digits are the ones you add.

Check it the way the rule says: pick any row, column or box and you will find 1 to 9, once each.

Habits that make the next puzzle easier

• Start where it is crowded. A row with two gaps is nearly solved. A row with seven gaps is not the place to start.
• Use all three directions. Each square belongs to one row, one column and one box. A digit you miss in the row is often sitting in the box.
• Follow your last move. A new digit changes its row, its column and its box. Look there first.
• Don't guess. On an easy puzzle there is always a square with only one possibility. If you can't find one, the answer is to look again, not to guess. A wrong guess hides itself for many moves and then breaks the grid.
• Write notes when you need them. Small pencilled candidates stop you checking the same square twice. Our guide to pencil marks shows how to keep them useful.

Where to go from here

Play a few puzzles on the easy page using only what you saw here. When you finish them without hints, move to medium and practise scanning by digit. The techniques page lists every method our puzzles use, in the order you will meet them.