How to Solve Sudoku: A Practical Beginner’s Guide

Learn the three constraints, a safe first move, and the difference between a single candidate and a single position.

How to solve Sudoku, one certain move at a time

You do not need arithmetic or a good memory to learn how to solve Sudoku. You need a way to answer a small question: which number is forced here, and what rules force it? Start with a verified Easy puzzle, keep the board in view, and make one move you can explain. Speed comes later.

A classic puzzle has nine rows, nine columns and nine boxes. A box is one of the nine regions outlined by thicker lines. Fill every empty cell with a digit from 1 to 9. Each row, column and box must contain every digit exactly once. The printed numbers are fixed clues. A number you enter is your proposed answer; a small pencil mark records a possibility.

The worked positions below come from our own verified puzzles. Some show a puzzle partway through its solution. The figures include the full logical candidates for those positions. Their numbers do not change when you change language. We describe a cell as r1c5: row 1, column 5, counted from the top left.

Look across three constraints

Choose one empty cell. List the digits missing from its row, then cross out anything already in its column or box. A digit must pass all three tests. Passing only one is insufficient: a 4 that fits the row may still collide with a 4 below it.

In the first position, r1c5 sits in row 1, column 5 and the top middle box. Row 1 already contains 6, 9, 8, 2 and 7, so its missing digits are 1, 3, 4 and 5. Column 5 already contains 6, 8, 3 and 9, removing 3 from that list. Its box contains 9, 8, 1, 4, 6 and 3, removing 1 and 4. Only 5 passes every constraint.

Board overview

Beginner example: row 1 column 5 has only candidate 5 after checking its row, column and box.c1c2c3c4c5c6c7c8c9r1r2r3r4r5r6r7r8r93453456958213473578257157493647912763458123824714717961247951579682141431264735181278929247948524773616153891724124579145257234712471675828929

View the whole grid first. Zoom in to read candidates and their coordinates.

Enlarge candidates

Choose a box to read its candidates and coordinates.

Beginner example: row 1 column 5 has only candidate 5 after checking its row, column and box. · Box 1c1c2c3r1r2r3345345635782574791
Original Easy position: r1c5 has one legal candidate, 5. The highlighted cell belongs to three overlapping regions.

You can enter 5 without deciding anything about the other blanks. This is a naked single. “Single” describes the remaining candidate, not the number of empty cells in the row. A row can have several blanks while one of them is already forced.

After placing a number, revisit its neighbors. A neighbor is any cell in the same row, column or box. None may still contain that number as a candidate. In this example, placing 5 also removes 5 from the candidates of other empty cells in row 1, column 5 and the top middle box. It may expose your next move.

Board overview

After the first certain move: 5 is placed at row 1 column 5 and neighboring candidates update.c1c2c3c4c5c6c7c8c9r1r2r3r4r5r6r7r8r93434695821347357825717493647912763458123824714717961247951579682141431264735181278929247948524773616153891724124579145257234712471675828929

View the whole grid first. Zoom in to read candidates and their coordinates.

Enlarge candidates

Choose a box to read its candidates and coordinates.

After the first certain move: 5 is placed at row 1 column 5 and neighboring candidates update. · Box 1c1c2c3r1r2r33434635782574791
After r1c5 = 5, neighboring possibilities change. Read the new position before choosing another number.

Ask where a digit must go

A useful second approach reverses the question. Instead of asking what can go in one cell, ask where a particular digit can go in one whole row, column or box. The unit needs that digit somewhere. If only one cell can accept it, that cell is forced even if it has other candidates.

In our second position, r2c5 has candidates 3 and 6. That does not make it a naked single. But row 2 needs a 3, and no other empty cell in row 2 can accept 3. Therefore r2c5 must be 3. This is a hidden single: the certain placement is hidden among the cell’s other candidates.

Board overview

Hidden single example: 3 has exactly one candidate position in row 2, at column 5, whose cell candidates are 3 and 6.c1c2c3c4c5c6c7c8c9r1r2r3r4r5r6r7r8r93248246782569124678946782456791695836712464612461678128126784695636781256795789458478935256846781346726147835134584789347183148714692468524616121269531467467847691825363691589158367419219

View the whole grid first. Zoom in to read candidates and their coordinates.

Enlarge candidates

Choose a box to read its candidates and coordinates.

Hidden single example: 3 has exactly one candidate position in row 2, at column 5, whose cell candidates are 3 and 6. · Box 1c1c2c3r1r2r33248246781695167812812678
Ask about 3 across all of row 2. Its only position is r2c5, even though that cell also has candidate 6.

Board overview

After the hidden single: r2c5 contains 3 and its former candidate 6 is gone.c1c2c3c4c5c6c7c8c9r1r2r3r4r5r6r7r8r932482467825691246789467824567916958371246461246167812812678469563678125679578945847893525684678134672614783514584789347183148714692468524616121269531467467847691825363691589158367419219

View the whole grid first. Zoom in to read candidates and their coordinates.

Enlarge candidates

Choose a box to read its candidates and coordinates.

After the hidden single: r2c5 contains 3 and its former candidate 6 is gone. · Box 1c1c2c3r1r2r33248246781695167812812678
The row argument fills 3 at r2c5. Other cells in its row, column and box also lose candidate 3.

Do not conclude that a digit has one position because you wrote its pencil mark only once. First check every empty cell in the unit. Incomplete notes can hide a second legal position. The pencil marks guide explains how to keep this distinction clear.

A repeatable routine for how to solve Sudoku

If you are working out how to solve Sudoku without filling every cell with notes, use the following cycle:

  1. Look for a row, column or box with few empty cells. Write its missing digits mentally or on paper.
  2. Test each blank against the other two regions that cross it. Enter a number only when those constraints leave one option.
  3. Choose a digit that already appears several times. Inspect a box it has not reached and rule out rows and columns containing that digit.
  4. After a placement, examine its neighbors again. The newest information often makes a nearby move easier to see.
  5. When scanning stops producing clear moves, write complete candidates for a small area, then widen that area as needed.

There is no required order. You may find a different correct move from the published walkthrough. A sound Sudoku deduction remains sound whichever correct moves you found earlier. The game’s Hint examines your current entries rather than telling you to retrace a fixed sequence.

Two exercises: make the move and name the reason

For the first exercise, inspect r2c5 after the previous Easy placement. Choose the one digit that remains legal there. Explain which of its row, column and box restrictions remove the alternatives before checking your answer.

Loading puzzle…

Answer: r2c5 = 7. It is a naked single because the complete candidate list for that cell contains only 7. The explanation concerns one cell’s possible digits; it does not require row 2 to have only one blank.

For the second exercise, examine column 4 in the displayed position. Which digit has only one position in that column? Look at every empty cell before deciding.

Loading puzzle…

Answer: r1c4 = 2. The cell has candidates 2 and 5, but 2 can occur nowhere else in column 4. The column requires a 2, so the competing 5 cannot occupy that cell. Read the comparison of the two singles if these reasons still feel similar.

When two candidates remain, stop there

A cell with candidates 2 and 7 is unresolved. Choosing 2 because it looks more convenient creates a guess, not a deduction. Later contradictions may reveal that guess, but you will then need to remember every dependent move. Early practice is more useful when you preserve the uncertainty and look elsewhere.

If you stall, first check for duplicate entries and missing candidates. Then repeat the two questions: “What fits this cell?” and “Where must this digit go in this unit?” A staged Hint can point out an area, explain the reason and offer a step you can apply. Check compares existing entries with the verified answer; it does not fill your blanks. See the stuck-puzzle routine when basic scanning no longer moves the board forward.

Knowing how to solve Sudoku means recognizing evidence you can trust, including when the evidence is not yet enough. Finish a few Easy boards at your own pace, then try Medium when you want to practice candidate eliminations. You can also choose today’s three challenges, save one on this device and return to it later. There is no need to race a timer to make a correct move.

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