How sudoku works
The rules fit on one line: fill the grid so that every row, every column and every box contains all the numbers with none repeated. In a classic 9×9 sudoku that means 1 to 9, and the boxes are the nine 3×3 blocks marked with thicker lines.
That is all. Nothing gets added up, no maths is required, and the numbers could just as well be nine colours or nine letters without changing the puzzle: all that matters is that they are nine distinct symbols. Sudoku is pure logic, which is where its reputation for being approachable comes from.
A well-built sudoku never forces you to guess. If at any point you feel you have to try your luck, it almost always means there is a deduction you have not spotted yet.
Five techniques that solve almost any sudoku
The first two will get you through the easy ones entirely. The next three are what you need when the clues thin out.
1. The last empty cell
Look for rows, columns or boxes with only one cell missing. The number that goes there is the one that is not already present. It is the silliest technique and the most often missed: sweep the board for it every time you place something new.
2. The only candidate
Pick an empty cell and mentally cross off everything that already appears in its row, its column and its box. If only one number survives, that number goes there, with complete certainty. This is the technique that solves the most cells on easy and medium.
3. Cross-hatching
Change the question: instead of asking «what goes in this cell», ask «where can this number go». Take a number, say 7, and walk through the boxes that do not have one yet. In each, rule out the rows and columns that already contain a 7. Very often a single free cell is left in the whole box, solving a gap that cell-by-cell scanning never revealed.
This is the technique that separates a forty-minute solve from a ten-minute one.
4. Naked pairs
If within one box (or row, or column) there are two cells whose only candidates are the same pair of numbers — say both can only be 4 or 9 — then 4 and 9 occupy those two cells, even though you do not yet know in which order. And that lets you rule 4 and 9 out of every other cell in that box. It sounds like little and it unlocks a great deal.
5. Pencil marks, but sparingly
From medium upwards memory runs out and you have to note candidates. The classic mistake is noting every candidate in every cell from the start: you end up with an unreadable board. Better to mark only where you have narrowed things to two or three possibilities, which is where the note earns its place. On this page the pencil toggles with the ✏️ button or the N key, and committing a final number clears it from the marks in its row, column and box.
The mistakes that come up most
- Placing on a hunch. If you cannot explain why a number belongs in a cell, do not write it. A wrong number placed in minute two goes unnoticed until minute twenty, and by then you have no idea which one it was.
- Only ever looking at cells, never at numbers. Alternating between the two questions — «what goes here» and «where does this number go» — is what breaks a deadlock.
- Walking away from the row you nearly finished. Every number you place changes the possibilities in its row, column and box. After placing one, look right there again before moving elsewhere.
- Starting on hard. If you always stall at the same point, drop a level and work out which deduction you were missing. You learn far more that way than by grinding.
About the levels on this page
There are five. The 4×4 and 6×6 are not decoration: they are the best way to grasp the rule if you have never done a sudoku, and they work very well with children, because a 4×4 takes two minutes and the sense of having cracked it is identical. The three 9×9 levels differ in how many clues you start with: 40 on easy, 32 on medium and 26 on hard.
It is worth being honest about that measure: the clue count is an approximation, not an exact difficulty scale. What really determines how hard a sudoku is, is which techniques it demands and how the clues are spread, not how many there are. A badly spread 30-clue grid can cost more than a 26-clue one. What is guaranteed is that every one has a single solution: each was checked as it was generated.