How to solve Sudoku: a beginner’s guide

1 September 2026 · 8 min read

Sudoku looks like a maths puzzle and isn’t one. You never add anything up. The digits 1 to 9 are just nine distinguishable symbols; you could play with nine colours or nine animals and nothing would change. What the puzzle actually asks for is careful elimination, and that is a skill you can learn in an afternoon.

The only rule

Fill the 9×9 grid so that each digit 1 to 9 appears exactly once in every row, every column, and every one of the nine 3×3 boxes. Those 27 groups — nine rows, nine columns, nine boxes — are called units, and almost every technique in Sudoku is really a statement about one unit.

A well-made puzzle has exactly one solution, and that solution can always be reached by reasoning alone. You should never have to guess. If you find yourself guessing, either the puzzle is badly made or there is a deduction you haven’t spotted yet — and it is almost always the second one.

Learn the vocabulary first

Two words do most of the work, and both are worth learning before any technique:

• A candidate is a digit that could still legally go in a particular empty cell. A cell starts with up to nine candidates and loses them as the grid fills up.
• A cell’s peers are the other cells that share a unit with it — the eight others in its row, the eight in its column, and the eight in its box. Overlaps mean 20 distinct peers. A digit placed in a cell is instantly impossible in all 20.

Every technique on this site is a way of squeezing information out of that second fact. Here is one cell and its twenty peers:

Technique one: look for a cell with one option left

Pick an empty cell. Write down the digits already present in its row, its column and its box. If eight distinct digits turn up, the ninth is forced. That is a naked single, and it is the single most common move in Sudoku.

In the grid above, take the shaded cell in row 3, column 7. Row 3 already holds 3, 1, 4 and 9. Column 7 holds 6 and 5. The top-right box holds 6, 5 and 9. Put those together and 1, 3, 4, 5, 6 and 9 are all spoken for — and 7 and 8 are ruled out too, further along the same lines. Only 2 survives.

Technique two: look for a digit with one home left

Now turn the question around. Instead of asking “what can go in this cell?”, ask “where can this digit go in this box?” Take one digit and one unit, and cross off every cell in the unit that already sees that digit somewhere in its row, column or box. If exactly one cell survives, the digit belongs there — even if that cell still has several candidates of its own.

That is a hidden single, and it is where beginners make their first real jump. It is harder to see than a naked single because nothing about the cell looks special; the information is in the unit, not the cell. Boxes are the easiest place to start hunting, because a box is compact enough to take in at a glance.

These two techniques between them will finish essentially every puzzle labelled Easy. Both are worked through in detail here, with grids for each.

How to scan a grid without going in circles

The mistake almost everyone makes at first is wandering: look at a cell, look at another cell, lose track, start again. Scan systematically instead.

1. Start with the digit that appears most often. Count the 1s, the 2s and so on. Whichever digit is already placed six or seven times is the most constrained, and so the most likely to be forced somewhere.
2. Take that digit through all nine boxes. For each box that doesn’t have it yet, see whether the rows and columns already containing it leave only one possible cell.
3. Work the densest units. A row with seven digits filled is far more promising than one with three. Same for boxes and columns.
4. After every placement, re-scan its peers. A new digit changes 20 cells. The move that unlocks the next one is nearly always next door to the move you just made.

Here is an easy puzzle to try it on. Every cell in it can be filled by naked singles alone — no notation, no advanced patterns, no guessing.

When to start writing pencil marks

Pencil marks are the small candidate digits you write into empty cells. They are essential later and a waste of time early: on an easy puzzle you will finish before the marking pays for itself.

The right moment is the first time you go all the way round the grid and place nothing. That is the signal that you have exhausted what you can hold in your head and need the candidates written down. How to mark up a grid without drowning in digits covers doing that properly.

What to do when you’re stuck

Work through this list in order. It is roughly the order of increasing effort.

1. Re-scan the last digit you placed. Cheap, and it works surprisingly often.
2. Do a full digit sweep. All nine digits, all nine boxes. Slow, boring, and it finds hidden singles you skimmed past.
3. Check for a two-candidate cell you can pair up. Two cells in one unit holding the same two candidates lock those digits out of the rest of the unit — a naked pair.
4. Check the box/line intersections. If a digit is confined to one line within a box, it clears off that line elsewhere — and the reverse also holds. See pointing pairs and box/line reduction.
5. Only then reach for the fancy stuff. Patterns like the X-wing are real and useful, but hunting for one before you have swept for singles is how people spend twenty minutes finding a move that a ten-second scan would have handed them.

One thing not on the list: guessing. Writing in a digit to “see what happens” means that when you hit a contradiction forty moves later you cannot tell whether the guess was wrong or your reasoning since was. If you are genuinely out of ideas, the honest move is to press Explain next step on the board and have the deduction shown to you — you learn the pattern, and the grid stays trustworthy.

What good practice looks like

Speed comes from pattern recognition, and pattern recognition comes from seeing the same shapes repeatedly with the reasoning attached. Two habits are worth more than volume:

• Never place a digit you cannot justify in a sentence. “9 goes here because it is already in the other two rows of this box and column 4 is taken” is a reason. “It feels right” is not, and one unjustified digit can waste the next twenty minutes.
• When you get stuck and find the move, name it. Knowing you just used a hidden single in a column is what makes you find the next one faster. This is the whole reason this site explains moves rather than just revealing them.

Stay on Easy until you finish without notation. Move to Medium when hidden singles come quickly. Only go to Hard once you are comfortable writing pencil marks, because Hard is defined by needing them. What actually makes a puzzle hard explains why clue count is a poor guide to difficulty.

Every diagram on this page is a real position from a generated puzzle, and every elimination shown is checked against that puzzle’s unique solution as part of the test suite. Want a move explained on your own board? Play a puzzle.