Puzzle Learning Centre

How to Play Sudoku: A Complete Beginner’s Guide

Sudoku needs no arithmetic and no luck: just a pencil, a little patience and one simple rule. This guide takes you from your very first number to a complete puzzle solved step by step.

The grid

A Sudoku grid is a square of 81 smaller squares. Some already hold a digit; these are the clues, and they never change. Your job is to fill in the rest. The grid is divided three ways, and every rule of the game is about these three kinds of group:

Row. A row runs across: nine squares from left to right.

Column. A column runs down: nine squares from top to bottom.

Box. A box is one of the nine 3×3 blocks marked by the thicker lines.

In this guide we name squares by their row and column: R3C5 means row 3 (counting down from the top), column 5 (counting from the left). Boxes are numbered 1 to 9 like reading a page: box 1 is top left, box 3 top right and box 9 bottom right.

The rules

Fill each empty square with one digit from 1 to 9.
Every row must contain each digit from 1 to 9 exactly once.
Every column must contain each digit from 1 to 9 exactly once.
Every 3×3 box must contain each digit from 1 to 9 exactly once.

That’s all. Because each group holds nine squares and needs nine different digits, no digit can ever repeat within a row, a column or a box. The digits are only symbols; you never add them up. A well-made puzzle has exactly one solution, and you can reach it by reasoning alone, without guessing.

How to begin

Here is the puzzle we’ll use throughout this guide. It has 34 clues, a comfortable number for a first puzzle.

The practice puzzle, starting position
7	empty	empty	1	empty	empty	empty	empty	9
empty	3	empty	empty	7	9	2	empty	empty
1	6	9	empty	3	empty	empty	empty	empty
2	9	6	empty	empty	3	8	empty	empty
empty	empty	empty	6	empty	2	empty	empty	empty
empty	empty	4	5	empty	empty	7	2	6
empty	empty	empty	empty	2	empty	6	1	8
empty	empty	1	4	6	empty	empty	7	empty
6	empty	empty	empty	empty	1	empty	empty	5

The practice puzzle: 34 clues, 47 squares to fill.

Use a pencil, or a pen you can live with. You’ll want to make small notes.
Look for groups that are already nearly full. A row with seven clues has only two gaps to think about.
Pick one digit, say 1, and look at every box in turn: where could a 1 still go? Then try the next digit.
Only write a digit in when you can say why it must go there. If you can’t, leave it and look elsewhere.

Your first number

Let’s look at R2C4, an empty square in row 2, column 4 and box 2. Instead of asking “what goes here?”, ask “what can’t go here?”

R2C4 and the clues that see it
7	empty	empty	1 (used in the reasoning)	empty	empty	empty	empty	9
empty	3 (used in the reasoning)	empty	highlighted empty square	7 (used in the reasoning)	9 (used in the reasoning)	2 (used in the reasoning)	empty	empty
1	6	9	empty	3	empty	empty	empty	empty
2	9	6	empty	empty	3	8	empty	empty
empty	empty	empty	6 (used in the reasoning)	empty	2	empty	empty	empty
empty	empty	4	5 (used in the reasoning)	empty	empty	7	2	6
empty	empty	empty	empty	2	empty	6	1	8
empty	empty	1	4 (used in the reasoning)	6	empty	empty	7	empty
6	empty	empty	empty	empty	1	empty	empty	5

R2C4 is highlighted. The ringed clues in its row, column and box rule out every digit but 8.

Row 2 already has 2, 3, 7 and 9.
Column 4 already has 1, 4, 5 and 6, which adds 1, 4, 5 and 6.
Box 2 already has 1, 3, 7 and 9, but nothing we haven’t already ruled out.

Together they account for eight different digits. The only one left is 8, so R2C4 must be 8. Write it in: you’ve placed your first number.

Technique 1: naked singles

What you just did has a name. When a square’s row, column and box between them rule out eight digits, the ninth is the only possibility. Solvers call it a naked single: one candidate, plain to see.

Here’s another. For R4C4, check each digit from 1 to 9 against the square’s row, column and box:

R4C4 and the clues that see it
7	empty	empty	1 (used in the reasoning)	empty	empty	empty	empty	9
empty	3	empty	empty	7	9	2	empty	empty
1	6	9	empty	3	empty	empty	empty	empty
2 (used in the reasoning)	9 (used in the reasoning)	6 (used in the reasoning)	highlighted empty square	empty	3 (used in the reasoning)	8 (used in the reasoning)	empty	empty
empty	empty	empty	6	empty	2	empty	empty	empty
empty	empty	4	5 (used in the reasoning)	empty	empty	7	2	6
empty	empty	empty	empty	2	empty	6	1	8
empty	empty	1	4 (used in the reasoning)	6	empty	empty	7	empty
6	empty	empty	empty	empty	1	empty	empty	5

R4C4, with the clues that rule out each other digit ringed.

1in column 4 (R1C4)
2in row 4 (R4C1)
3in row 4 (R4C6)
4in column 4 (R8C4)
5in column 4 (R6C4)
6in row 4 (R4C3)
7the only one left
8in row 4 (R4C7)
9in row 4 (R4C2)

Naked single: list what a square’s row, column and box already contain. If only one digit is missing from that list, it goes in the square.

Technique 2: hidden singles

Sometimes a square could still hold several digits, yet one of them has nowhere else to go. Turn the question around: pick a group and a digit it still needs, and ask where that digit can go.

Box 2 has no 6 yet. Look at its empty squares one by one:

Where can the 6 go in box 2?
7	empty	empty	1	ruled out	highlighted empty square	empty	empty	9
empty	3	empty	ruled out	7	9	2	empty	empty
1	6 (used in the reasoning)	9	ruled out	3	ruled out	empty	empty	empty
2	9	6	empty	empty	3	8	empty	empty
empty	empty	empty	6 (used in the reasoning)	empty	2	empty	empty	empty
empty	empty	4	5	empty	empty	7	2	6
empty	empty	empty	empty	2	empty	6	1	8
empty	empty	1	4	6 (used in the reasoning)	empty	empty	7	empty
6	empty	empty	empty	empty	1	empty	empty	5

Box 2 is shaded. Crossed squares are ruled out by the ringed 6s; only R1C6 is left.

R1C5 can’t take a 6: column 5 already has one, at R8C5.
R2C4 can’t take a 6: column 4 already has one, at R5C4.
R3C4 can’t take a 6: row 3 already has one, at R3C2.
R3C6 can’t take a 6: row 3 already has one, at R3C2.
That leaves R1C6, the only place in box 2 where a 6 can go.

Notice that R1C6 on its own could still be 4, 5, 6 or 8, so it isn’t a naked single. It’s a hidden single: the 6 is forced because box 2 has no other place for it. The same reasoning works for any row and column too.

Pencil marks

On harder puzzles you’ll want to keep track of what each square could still be. Write the possibilities small in the corner of the square: these are pencil marks (also called candidates). When you place a digit, rub it out of the pencil marks in the same row, column and box.

Before placing the 6

The squares of row 1, with pencil marks in each empty one:

R1C17 (filled)
R1C22458
R1C3258
R1C41 (filled)
R1C5458
R1C64568
R1C7345
R1C834568
R1C99 (filled)

After placing 6 in R1C6

The new 6 sees the whole of row 1, so every other 6 in its pencil marks is crossed out (R1C8).

R1C17 (filled)
R1C22458
R1C3258
R1C41 (filled)
R1C5458
R1C66 (filled)
R1C7345
R1C8345~~6 (removed)~~8
R1C99 (filled)

Keep pencil marks tidy and always put each digit in the same spot (1 top left, 9 bottom right). Your eye then spots a square with a single mark, or a digit that appears only once in a group, at a glance.

Common mistakes

Guessing
A guess that happens to fit can still be wrong, and you may not find out for twenty moves. If you can’t explain a placement, don’t make it.
Checking only two of the three groups
It’s easy to check the row and column and forget the box (or the other way round). Every square belongs to all three.
Forgetting to update pencil marks
Stale marks lead to false conclusions. Each time you write a digit in, clear it from the marks in its row, column and box.
Mixing up rows and columns
Rows run across, columns run down. Naming squares as R(row)C(column), always in that order, helps.
Adding the numbers up
Sudoku digits are just symbols. You never need to add them; that’s Kakuro.

A complete worked puzzle

Now let’s solve the whole practice puzzle. It takes 47 placements: 19 naked singles and 28 hidden singles. Each step names the square, the digit, the technique and the group that proves it. Every grid along the way is valid, and every step follows from the one before.

Sudoku grid, starting position
7	empty	empty	1	empty	empty	empty	empty	9
empty	3	empty	empty	7	9	2	empty	empty
1	6	9	empty	3	empty	empty	empty	empty
2	9	6	empty	empty	3	8	empty	empty
empty	empty	empty	6	empty	2	empty	empty	empty
empty	empty	4	5	empty	empty	7	2	6
empty	empty	empty	empty	2	empty	6	1	8
empty	empty	1	4	6	empty	empty	7	empty
6	empty	empty	empty	empty	1	empty	empty	5

Starting position

Ready when you are

In each step, the square with the heavy border is the one being filled. Shading marks the row, column or box being used, ringed digits are the clues the reasoning relies on, and × marks squares that are ruled out. Try to spot each placement yourself before pressing “Next step”.

Read all 47 steps as text

2 in R3C4: hidden single in box 2. Box 2 still needs a 2. Its other empty squares can’t take it: R1C5 (column 5 already has a 2), R1C6 (column 6 already has a 2), R2C4 (row 2 already has a 2) and R3C6 (column 6 already has a 2). So the 2 must go in R3C4.
6 in R1C6: hidden single in box 2. Box 2 still needs a 6. Its other empty squares can’t take it: R1C5 (column 5 already has a 6), R2C4 (column 4 already has a 6) and R3C6 (row 3 already has a 6). So the 6 must go in R1C6.
1 in R2C9: hidden single in box 3. Box 3 still needs a 1. Its other empty squares can’t take it: R1C7 (row 1 already has a 1), R1C8 (row 1 already has a 1), R2C8 (column 8 already has a 1), R3C7 (row 3 already has a 1), R3C8 (row 3 already has a 1) and R3C9 (row 3 already has a 1). So the 1 must go in R2C9.
6 in R2C8: hidden single in box 3. Box 3 still needs a 6. Its other empty squares can’t take it: R1C7 (row 1 already has a 6), R1C8 (row 1 already has a 6), R3C7 (row 3 already has a 6), R3C8 (row 3 already has a 6) and R3C9 (row 3 already has a 6). So the 6 must go in R2C8.
7 in R3C9: hidden single in box 3. Box 3 still needs a 7. Its other empty squares can’t take it: R1C7 (row 1 already has a 7), R1C8 (row 1 already has a 7), R3C7 (column 7 already has a 7) and R3C8 (column 8 already has a 7). So the 7 must go in R3C9.
1 in R5C7: hidden single in box 6. Box 6 still needs a 1. Its other empty squares can’t take it: R4C8 (column 8 already has a 1), R4C9 (column 9 already has a 1), R5C8 (column 8 already has a 1) and R5C9 (column 9 already has a 1). So the 1 must go in R5C7.
1 in R6C2: hidden single in box 4. Box 4 still needs a 1. Its other empty squares can’t take it: R5C1 (row 5 already has a 1), R5C2 (row 5 already has a 1), R5C3 (row 5 already has a 1) and R6C1 (column 1 already has a 1). So the 1 must go in R6C2.
1 in R4C5: hidden single in box 5. Box 5 still needs a 1. Its other empty squares can’t take it: R4C4 (column 4 already has a 1), R5C5 (row 5 already has a 1), R6C5 (row 6 already has a 1) and R6C6 (row 6 already has a 1). So the 1 must go in R4C5.
4 in R5C5: hidden single in box 5. Box 5 still needs a 4. Its other empty squares can’t take it: R4C4 (column 4 already has a 4), R6C5 (row 6 already has a 4) and R6C6 (row 6 already has a 4). So the 4 must go in R5C5.
4 in R3C6: hidden single in box 2. Box 2 still needs a 4. Its other empty squares can’t take it: R1C5 (column 5 already has a 4) and R2C4 (column 4 already has a 4). So the 4 must go in R3C6.
5 in R1C5: hidden single in box 2. Box 2 still needs a 5. Its other empty squares can’t take it: R2C4 (column 4 already has a 5). So the 5 must go in R1C5.
9 in R6C5: hidden single in box 5. Box 5 still needs a 9. Its other empty squares can’t take it: R4C4 (row 4 already has a 9) and R6C6 (column 6 already has a 9). So the 9 must go in R6C5.
9 in R5C8: hidden single in box 6. Box 6 still needs a 9. Its other empty squares can’t take it: R4C8 (row 4 already has a 9), R4C9 (row 4 already has a 9) and R5C9 (column 9 already has a 9). So the 9 must go in R5C8.
5 in R4C8: hidden single in box 6. Box 6 still needs a 5. Its other empty squares can’t take it: R4C9 (column 9 already has a 5) and R5C9 (column 9 already has a 5). So the 5 must go in R4C8.
2 in R8C9: hidden single in box 9. Box 9 still needs a 2. Its other empty squares can’t take it: R8C7 (column 7 already has a 2), R9C7 (column 7 already has a 2) and R9C8 (column 8 already has a 2). So the 2 must go in R8C9.
8 in R2C4: naked single. Row 2 shows 1, 2, 3, 6, 7 and 9; column 4 adds 4 and 5. That accounts for eight different digits, so R2C4 can only be 8.
5 in R2C3: naked single. Row 2 shows 1, 2, 3, 6, 7, 8 and 9; column 3 adds 4. That accounts for eight different digits, so R2C3 can only be 5.
4 in R2C1: naked single. Row 2 shows 1, 2, 3, 5, 6, 7, 8 and 9. That accounts for eight different digits, so R2C1 can only be 4.
5 in R3C7: naked single. Row 3 shows 1, 2, 3, 4, 6, 7 and 9; column 7 adds 8. That accounts for eight different digits, so R3C7 can only be 5.
8 in R3C8: naked single. Row 3 shows 1, 2, 3, 4, 5, 6, 7 and 9. That accounts for eight different digits, so R3C8 can only be 8.
7 in R4C4: naked single. Row 4 shows 1, 2, 3, 5, 6, 8 and 9; column 4 adds 4. That accounts for eight different digits, so R4C4 can only be 7.
7 in R7C6: hidden single in box 8. Box 8 still needs a 7. Its other empty squares can’t take it: R7C4 (column 4 already has a 7), R8C6 (row 8 already has a 7), R9C4 (column 4 already has a 7) and R9C5 (column 5 already has a 7). So the 7 must go in R7C6.
5 in R8C6: hidden single in box 8. Box 8 still needs a 5. Its other empty squares can’t take it: R7C4 (column 4 already has a 5), R9C4 (row 9 already has a 5) and R9C5 (row 9 already has a 5). So the 5 must go in R8C6.
4 in R4C9: naked single. Row 4 shows 1, 2, 3, 5, 6, 7, 8 and 9. That accounts for eight different digits, so R4C9 can only be 4.
3 in R5C9: naked single. Row 5 shows 1, 2, 4, 6 and 9; column 9 adds 5, 7 and 8. That accounts for eight different digits, so R5C9 can only be 3.
3 in R6C1: hidden single in box 4. Box 4 still needs a 3. Its other empty squares can’t take it: R5C1 (row 5 already has a 3), R5C2 (row 5 already has a 3) and R5C3 (row 5 already has a 3). So the 3 must go in R6C1.
8 in R6C6: naked single. Row 6 shows 1, 2, 3, 4, 5, 6, 7 and 9. That accounts for eight different digits, so R6C6 can only be 8.
3 in R7C3: naked single. Row 7 shows 1, 2, 6, 7 and 8; column 3 adds 4, 5 and 9. That accounts for eight different digits, so R7C3 can only be 3.
3 in R9C4: hidden single in box 8. Box 8 still needs a 3. Its other empty squares can’t take it: R7C4 (row 7 already has a 3) and R9C5 (column 5 already has a 3). So the 3 must go in R9C4.
3 in R8C7: hidden single in box 9. Box 9 still needs a 3. Its other empty squares can’t take it: R9C7 (row 9 already has a 3) and R9C8 (row 9 already has a 3). So the 3 must go in R8C7.
3 in R1C8: hidden single in box 3. Box 3 still needs a 3. Its other empty squares can’t take it: R1C7 (column 7 already has a 3). So the 3 must go in R1C8.
9 in R9C7: hidden single in box 9. Box 9 still needs a 9. Its other empty squares can’t take it: R9C8 (column 8 already has a 9). So the 9 must go in R9C7.
4 in R1C7: naked single. Row 1 shows 1, 3, 5, 6, 7 and 9; column 7 adds 2 and 8. That accounts for eight different digits, so R1C7 can only be 4.
9 in R7C4: naked single. Row 7 shows 1, 2, 3, 6, 7 and 8; column 4 adds 4 and 5. That accounts for eight different digits, so R7C4 can only be 9.
9 in R8C1: hidden single in box 7. Box 7 still needs a 9. Its other empty squares can’t take it: R7C1 (row 7 already has a 9), R7C2 (row 7 already has a 9), R8C2 (column 2 already has a 9), R9C2 (row 9 already has a 9) and R9C3 (row 9 already has a 9). So the 9 must go in R8C1.
5 in R7C1: naked single. Row 7 shows 1, 2, 3, 6, 7, 8 and 9; column 1 adds 4. That accounts for eight different digits, so R7C1 can only be 5.
5 in R5C2: hidden single in box 4. Box 4 still needs a 5. Its other empty squares can’t take it: R5C1 (column 1 already has a 5) and R5C3 (column 3 already has a 5). So the 5 must go in R5C2.
7 in R5C3: hidden single in box 4. Box 4 still needs a 7. Its other empty squares can’t take it: R5C1 (column 1 already has a 7). So the 7 must go in R5C3.
7 in R9C2: hidden single in box 7. Box 7 still needs a 7. Its other empty squares can’t take it: R7C2 (row 7 already has a 7), R8C2 (row 8 already has a 7) and R9C3 (column 3 already has a 7). So the 7 must go in R9C2.
2 in R9C3: hidden single in box 7. Box 7 still needs a 2. Its other empty squares can’t take it: R7C2 (row 7 already has a 2) and R8C2 (row 8 already has a 2). So the 2 must go in R9C3.
2 in R1C2: hidden single in box 1. Box 1 still needs a 2. Its other empty squares can’t take it: R1C3 (column 3 already has a 2). So the 2 must go in R1C2.
8 in R1C3: naked single. Row 1 shows 1, 2, 3, 4, 5, 6, 7 and 9. That accounts for eight different digits, so R1C3 can only be 8.
8 in R5C1: naked single. Row 5 shows 1, 2, 3, 4, 5, 6, 7 and 9. That accounts for eight different digits, so R5C1 can only be 8.
4 in R7C2: naked single. Row 7 shows 1, 2, 3, 5, 6, 7, 8 and 9. That accounts for eight different digits, so R7C2 can only be 4.
8 in R8C2: naked single. Row 8 shows 1, 2, 3, 4, 5, 6, 7 and 9. That accounts for eight different digits, so R8C2 can only be 8.
8 in R9C5: naked single. Row 9 shows 1, 2, 3, 5, 6, 7 and 9; column 5 adds 4. That accounts for eight different digits, so R9C5 can only be 8.
4 in R9C8: naked single. Row 9 shows 1, 2, 3, 5, 6, 7, 8 and 9. That accounts for eight different digits, so R9C8 can only be 4.

Tips for improving

Scan methodically. Take each digit from 1 to 9 in turn and look for hidden singles in every box.
Look for groups with only one or two gaps first; they are the quickest wins.
When you’re stuck, fill in pencil marks for a whole box or row. Patterns appear that were invisible before.
Take a break. A fresh look often reveals a single you’d walked straight past.
Check your finished grid: every row, column and box should contain 1 to 9 once each.

A puzzle to try

Ready for one on your own? This puzzle is new: it isn’t the one solved above. Every square can be filled with the two techniques from this guide, naked singles and hidden singles, so you never need to guess.

Sudoku: a puzzle to try

34 clues. Fill every row, column and box with the digits 1 to 9.

A Sudoku to try, starting position
1	empty	5	empty	empty	3	empty	empty	empty
empty	6	empty	8	empty	9	empty	empty	empty
7	empty	empty	empty	empty	empty	empty	3	empty
6	7	empty	5	8	2	empty	1	4
empty	1	2	empty	empty	empty	8	7	empty
4	9	empty	6	1	7	empty	2	3
empty	5	empty	empty	empty	empty	empty	empty	9
empty	empty	empty	9	empty	5	empty	8	empty
empty	empty	empty	1	empty	empty	3	empty	5

Answer

The answer to the Sudoku to try
1	8 (solved)	5	2 (solved)	6 (solved)	3	4 (solved)	9 (solved)	7 (solved)
3 (solved)	6	4 (solved)	8	7 (solved)	9	1 (solved)	5 (solved)	2 (solved)
7	2 (solved)	9 (solved)	4 (solved)	5 (solved)	1 (solved)	6 (solved)	3	8 (solved)
6	7	3 (solved)	5	8	2	9 (solved)	1	4
5 (solved)	1	2	3 (solved)	9 (solved)	4 (solved)	8	7	6 (solved)
4	9	8 (solved)	6	1	7	5 (solved)	2	3
8 (solved)	5	1 (solved)	7 (solved)	3 (solved)	6 (solved)	2 (solved)	4 (solved)	9
2 (solved)	3 (solved)	6 (solved)	9	4 (solved)	5	7 (solved)	8	1 (solved)
9 (solved)	4 (solved)	7 (solved)	1	2 (solved)	8 (solved)	3	6 (solved)	5

From the free guide at northfinchpress.com/sudoku/how-to-play · Northfinch Press

Show the answer

The answer to the Sudoku to try
1	8 (solved)	5	2 (solved)	6 (solved)	3	4 (solved)	9 (solved)	7 (solved)
3 (solved)	6	4 (solved)	8	7 (solved)	9	1 (solved)	5 (solved)	2 (solved)
7	2 (solved)	9 (solved)	4 (solved)	5 (solved)	1 (solved)	6 (solved)	3	8 (solved)
6	7	3 (solved)	5	8	2	9 (solved)	1	4
5 (solved)	1	2	3 (solved)	9 (solved)	4 (solved)	8	7	6 (solved)
4	9	8 (solved)	6	1	7	5 (solved)	2	3
8 (solved)	5	1 (solved)	7 (solved)	3 (solved)	6 (solved)	2 (solved)	4 (solved)	9
2 (solved)	3 (solved)	6 (solved)	9	4 (solved)	5	7 (solved)	8	1 (solved)
9 (solved)	4 (solved)	7 (solved)	1	2 (solved)	8 (solved)	3	6 (solved)	5

Quick rules to print

A one-page reminder to keep beside your puzzle book.

Sudoku: the quick rules

The grid has 81 squares: nine rows, nine columns and nine 3×3 boxes.
Fill every empty square with a digit from 1 to 9.
Each row must contain every digit from 1 to 9 exactly once.
Each column must contain every digit from 1 to 9 exactly once.
Each 3×3 box must contain every digit from 1 to 9 exactly once.
The starting numbers can’t be changed. A good puzzle has exactly one solution, reached by logic alone: no guessing or arithmetic needed.

Full illustrated guide: northfinchpress.com/sudoku/how-to-play · Northfinch Press

Kakuro
How to play Kakuro
Learn how sums, number combinations and intersecting runs work together.
Read the guide: How to play Kakuro
Futoshiki
How to play Futoshiki
Understand number placement, inequalities and deduction in a grid.
Read the guide: How to play Futoshiki

Back to the Puzzle Learning Centre