Foundations
Sudoku Rules — the 3 constraints
Sudoku has exactly three rules: every row, every column and every 3×3 box must contain the digits 1 to 9 exactly once each. That is the whole game — no arithmetic, no patterns to memorise, and never any guessing. Every technique in this course, from Naked Single to 3D Medusa, is only a faster way of seeing what those three constraints already force.
What you need to see on the grid
Before any technique makes sense, you need to see the grid the way solvers do: as 27 overlapping units, and as a coordinate system you can name out loud.
- Unit
- A row, a column or a 3×3 box. A grid has 27 of them — 9 rows, 9 columns, 9 boxes — and each one must end up holding 1 to 9 exactly once.
- Peers
- The 20 cells that share a row, a column or a box with a given cell. A cell can never hold a digit that one of its peers already holds — this single sentence is where every elimination comes from.
- Candidate
- A digit a cell could still legally take. Start with 1–9, cross off every digit already sitting in one of its peers, and what is left are the candidates.
- R4C7 notation
- Row 4, column 7, counting from the top-left corner. Every solution on this site uses it, and so does the hint inside the app — so a step you read here reads the same in your hand.
- Given
- A digit printed in the puzzle at the start. It never changes. If a technique ever tells you to change one, the technique was applied wrongly.
A worked example
Below is the first move the app's own hint engine makes on a real puzzle. It uses nothing but the three rules: the highlighted cell is shown together with everything it can see, and once those digits are crossed off only one candidate survives.
| · | · | 6 | 4 | · | · | 9 | · | · |
| 2 | 4 | · | 9 | · | 7 | · | · | 1 |
| · | · | 3 | · | 6 | 1 | · | 8 | 2 |
| · | 8 | 2 | · | 7 | 5 | · | 1 | · |
| · | 6 | 1 | · | 2 | · | · | 7 | 5 |
| · | · | · | 6 | · | 4 | 8 | 2 | · |
| 3 | 2 | 9 | 7 | 5 | · | · | · | · |
| 8 | · | 4 | 2 | 9 | · | · | 5 | 6 |
| 6 | · | · | · | · | 8 | · | 9 | 3 |
| · | · | 6 | 4 | · | · | 9 | · | · |
| 2 | 4 | 8 | 9 | · | 7 | · | · | 1 |
| · | · | 3 | · | 6 | 1 | · | 8 | 2 |
| · | 8 | 2 | · | 7 | 5 | · | 1 | · |
| · | 6 | 1 | · | 2 | · | · | 7 | 5 |
| · | · | · | 6 | · | 4 | 8 | 2 | · |
| 3 | 2 | 9 | 7 | 5 | · | · | · | · |
| 8 | · | 4 | 2 | 9 | · | · | 5 | 6 |
| 6 | · | · | · | · | 8 | · | 9 | 3 |
The engine calls this move Hidden Single — inside one row, column or box this digit fits in only one cell, so it must go there.
Practice puzzles
Each puzzle below was checked by the solver: all of them can be finished with the three rules alone, so nothing from later in the course is needed. Print them or solve on screen — the answer is one click away under each grid.
Puzzle 1 40 clues
| · | · | 8 | · | · | · | · | 5 | 6 |
| · | · | 7 | 4 | · | · | 2 | · | · |
| · | 5 | · | 2 | · | · | · | 1 | · |
| 7 | · | · | · | 4 | · | 8 | · | 1 |
| · | · | 9 | · | · | 1 | 7 | 3 | 5 |
| 8 | · | 1 | · | · | 5 | 6 | · | 9 |
| 9 | 6 | 2 | 1 | · | 3 | · | 7 | · |
| 1 | 8 | 3 | · | 7 | · | 9 | 6 | 2 |
| · | · | · | · | 6 | 2 | · | 8 | 3 |
Show the answer
| 2 | 9 | 8 | 3 | 1 | 7 | 4 | 5 | 6 |
| 3 | 1 | 7 | 4 | 5 | 6 | 2 | 9 | 8 |
| 4 | 5 | 6 | 2 | 9 | 8 | 3 | 1 | 7 |
| 7 | 3 | 5 | 6 | 4 | 9 | 8 | 2 | 1 |
| 6 | 4 | 9 | 8 | 2 | 1 | 7 | 3 | 5 |
| 8 | 2 | 1 | 7 | 3 | 5 | 6 | 4 | 9 |
| 9 | 6 | 2 | 1 | 8 | 3 | 5 | 7 | 4 |
| 1 | 8 | 3 | 5 | 7 | 4 | 9 | 6 | 2 |
| 5 | 7 | 4 | 9 | 6 | 2 | 1 | 8 | 3 |
Solved by the engine in 41 deductions — Hidden Single × 21 · Naked Single × 20.
Puzzle 2 38 clues
| · | · | · | · | 2 | · | 6 | · | · |
| · | · | · | 9 | 5 | 4 | 3 | · | 1 |
| 3 | · | 2 | 6 | 8 | · | · | 5 | 4 |
| 2 | · | · | · | · | 3 | · | 7 | · |
| 5 | · | 7 | · | 4 | · | · | · | · |
| · | 3 | · | 5 | · | 6 | · | · | · |
| 1 | · | · | · | 3 | 8 | · | 6 | 5 |
| 4 | · | 6 | 1 | 9 | 2 | 7 | · | · |
| · | 8 | 3 | · | 6 | 5 | 1 | · | · |
Show the answer
| 9 | 4 | 5 | 3 | 2 | 1 | 6 | 8 | 7 |
| 6 | 7 | 8 | 9 | 5 | 4 | 3 | 2 | 1 |
| 3 | 1 | 2 | 6 | 8 | 7 | 9 | 5 | 4 |
| 2 | 9 | 4 | 8 | 1 | 3 | 5 | 7 | 6 |
| 5 | 6 | 7 | 2 | 4 | 9 | 8 | 1 | 3 |
| 8 | 3 | 1 | 5 | 7 | 6 | 2 | 4 | 9 |
| 1 | 2 | 9 | 7 | 3 | 8 | 4 | 6 | 5 |
| 4 | 5 | 6 | 1 | 9 | 2 | 7 | 3 | 8 |
| 7 | 8 | 3 | 4 | 6 | 5 | 1 | 9 | 2 |
Solved by the engine in 43 deductions — Hidden Single × 23 · Naked Single × 20.
Puzzle 3 36 clues
| · | 4 | · | · | · | 8 | · | · | · |
| · | · | 8 | 6 | 7 | · | 3 | · | · |
| 6 | 7 | 5 | 9 | 4 | 3 | · | · | · |
| · | · | · | · | · | 1 | 6 | · | 7 |
| · | · | · | · | · | 9 | · | 3 | 2 |
| 2 | · | · | · | 8 | · | 9 | · | 4 |
| · | 1 | 7 | 5 | · | · | 2 | 9 | 3 |
| · | · | · | 3 | · | · | 7 | · | 8 |
| · | · | 2 | 8 | 1 | · | · | 6 | 5 |
Show the answer
| 9 | 4 | 3 | 1 | 2 | 8 | 5 | 7 | 6 |
| 1 | 2 | 8 | 6 | 7 | 5 | 3 | 4 | 9 |
| 6 | 7 | 5 | 9 | 4 | 3 | 8 | 2 | 1 |
| 4 | 5 | 9 | 2 | 3 | 1 | 6 | 8 | 7 |
| 7 | 8 | 6 | 4 | 5 | 9 | 1 | 3 | 2 |
| 2 | 3 | 1 | 7 | 8 | 6 | 9 | 5 | 4 |
| 8 | 1 | 7 | 5 | 6 | 4 | 2 | 9 | 3 |
| 5 | 6 | 4 | 3 | 9 | 2 | 7 | 1 | 8 |
| 3 | 9 | 2 | 8 | 1 | 7 | 4 | 6 | 5 |
Solved by the engine in 45 deductions — Hidden Single × 24 · Naked Single × 21.
Puzzle 4 34 clues
| 3 | 9 | 1 | 7 | 2 | · | 4 | · | · |
| · | 6 | · | · | · | · | 5 | · | 7 |
| · | · | · | · | 6 | 4 | · | · | 3 |
| · | · | · | 4 | · | · | 6 | · | · |
| · | 7 | 2 | · | · | · | 9 | · | 5 |
| · | · | · | 5 | 3 | 9 | · | · | · |
| · | · | 8 | 2 | 5 | · | 7 | · | · |
| 6 | · | 7 | · | · | 8 | · | 5 | 2 |
| · | 5 | 3 | · | · | 7 | · | 1 | · |
Show the answer
| 3 | 9 | 1 | 7 | 2 | 5 | 4 | 6 | 8 |
| 8 | 6 | 4 | 3 | 9 | 1 | 5 | 2 | 7 |
| 7 | 2 | 5 | 8 | 6 | 4 | 1 | 9 | 3 |
| 5 | 3 | 9 | 4 | 7 | 2 | 6 | 8 | 1 |
| 4 | 7 | 2 | 1 | 8 | 6 | 9 | 3 | 5 |
| 1 | 8 | 6 | 5 | 3 | 9 | 2 | 7 | 4 |
| 9 | 1 | 8 | 2 | 5 | 3 | 7 | 4 | 6 |
| 6 | 4 | 7 | 9 | 1 | 8 | 3 | 5 | 2 |
| 2 | 5 | 3 | 6 | 4 | 7 | 8 | 1 | 9 |
Solved by the engine in 47 deductions — Hidden Single × 28 · Naked Single × 19.
Common mistakes
Guessing when you get stuck
A well-formed Sudoku has exactly one solution and it is always reachable by deduction. Being stuck means you have missed a move, not that the puzzle wants a gamble. Go back to the unit with the fewest empty cells and re-check it.
Scanning rows and columns but forgetting the box
The box is the third constraint and it is the one that breaks most early deadlocks. A digit already in a box is gone from all nine of its cells — not just from its own row.
Writing a digit because it fits
"It fits here" is not a reason; "it fits nowhere else" is. A digit that merely fits may still belong to another cell in the same unit, and one wrong entry quietly poisons every deduction after it.
Try it on a real puzzle
Learn the move, not just the digit
Stuck on a real puzzle? The hint in the app names the technique it used and the cell it applies to, so you learn the move instead of just being handed the digit.