How to play Sudoku: rules, techniques and a practice plan

Sudoku looks like a numbers game. It is not — there is no arithmetic anywhere in it. It is a pattern game with nine symbols, and almost everyone who says they are “not good at numbers” turns out to be perfectly good at it once the scanning routine clicks.

The rules, in three sentences

Fill the 9×9 grid so that:

• every row contains 1–9 exactly once,
• every column contains 1–9 exactly once,
• and each of the nine 3×3 boxes contains 1–9 exactly once.

That is the whole rule set. The digits given at the start are clues, not a math problem. A well-formed puzzle has exactly one solution, which means every digit you place can be proved by logic — you never need to guess.

Before your first digit: build a scanning routine

Beginners lose by looking at the whole grid at once. Good solvers scan in a fixed order, and this is the single habit that separates a two-minute “I’m stuck” from a ten-minute solve.

The box-first scan. Pick the digit 1. Look at the three boxes in the top band. In each box ask: “where can a 1 go?” Cross out cells in boxes that already contain a 1, and cells in the same row or column as an existing 1. Repeat for 2, then 3, all the way to 9, then move to the next band. You will find two or three forced digits on almost any easy puzzle inside the first minute.

The row-completion scan. For each row with six or seven digits filled, list the missing digits and check which cells can legally hold them. This is where most “hidden singles” appear.

Technique 1 — naked single

Pick an empty cell and ask which digits it can legally hold. If exactly one digit remains, write it in. That is the whole technique.

The trap is doing it by eye. Work cell by cell across a row and physically cross out the digits already used in that cell’s row, column and box. Beginners stop at the first cell that looks easy; the reliable habit is to finish the row before moving on.

Technique 2 — hidden single

This is the technique that unlocks most stuck puzzles, and it is the one beginners skip.

Instead of asking “what fits this cell?”, ask “where in this box can a 7 go?” If every other cell in that box is blocked by a 7 in its row or column, the remaining cell holds the 7 — even if that cell could also hold three other digits.

Alternating between those two questions — naked single, hidden single — solves every easy puzzle and most mediums. Say them out loud as a pair: what fits here, where does this go.

Technique 3 — pencils and pairs

Once singles dry up, write candidate digits in the corners of empty cells (pencil marks). Two patterns are worth knowing:

Naked pair. Two cells in the same row, column or box contain exactly the same two candidates, for example {4,7} and {4,7}. Those two digits must occupy those two cells, so remove 4 and 7 from every other cell in that unit.

Hidden pair. Two digits appear in only two cells of a unit — say 3 and 9 appear nowhere else in that row. Those cells must hold 3 and 9, so every other candidate in them is wrong.

Both are eliminations, not placements. That is normal: at medium difficulty and above, half your progress comes from removing candidates rather than writing digits.

Technique 4 — locked candidates (pointing and claiming)

Take a box where every cell that can hold a 5 lies on the same row. Then the 5 for that box must be on that row, so no cell outside the box on that row can be a 5. That is pointing.

The reverse is claiming: if in a whole row the only cells that can hold a 5 sit inside one box, then that box’s 5 is somewhere on that row — so the rest of the box cannot contain a 5.

Locked candidates rarely place a digit immediately. What they do is collapse a board full of three-candidate cells into one full of singles.

Technique 5 — X-Wing

Look at a digit across two rows. In both rows, the digit has exactly two possible cells, and those cells sit in the same two columns. Then the digit forms a rectangle: it must occupy opposite corners, so it cannot appear anywhere else in those two columns.

X-Wing is the first technique that feels like a trick rather than an observation. It is worth learning because it appears constantly in hard puzzles, and the same shape generalised across three rows and columns is called a Swordfish.

Common mistakes

• Guessing early. One wrong digit invalidates everything downstream, and you will not notice for ten moves.
• Chasing a digit that is already placed. Before scanning for a 2, check you have not already found all nine 2s.
• Filling pencil marks by hand badly. Half-written candidates cause more errors than no candidates. If you use notes, keep them complete or erase them.
• Ignoring boxes. Rows and columns get all the attention; boxes are where forced digits hide.

A five-step practice plan

1. Ten easy puzzles, no pencil marks. Find every digit with singles only. The goal is speed of scanning, not solving.
2. Ten easy puzzles with notes on. Write every candidate before placing anything. Notice how often a digit appears only once.
3. Five medium puzzles, name the rule out loud for each placement. If you cannot name it, you guessed.
4. Learn one new technique per week — locked candidates first, then pairs, then X-Wing. Practise it on puzzles two levels below your comfort zone so the pattern is obvious.
5. Time yourself only after step 3. Speed is a by-product of a routine, and timing too early teaches you to guess.

How long should a puzzle take?

Easy 5–10 minutes, medium 10–20, hard 20–40. If an easy puzzle takes you forty minutes, the problem is almost always the scanning routine rather than the logic — go back to step one of the practice plan.

Frequently asked questions

Do I ever have to guess?

No. If you feel forced to guess, you have missed a hidden single, a locked candidate or a pair. Backtrack one move and rescans the unit you just changed.

Does Sudoku require maths?

No arithmetic, no equations. The digits are just nine distinguishable symbols; you could replace them with colours or letters and the puzzle would be identical.

Are all Sudoku puzzles uniquely solvable?

Only if they were generated correctly. A puzzle with multiple solutions is broken: it can be filled in several valid ways, so logic alone cannot decide between them. Our boards are checked for a unique solution before they are dealt.

What is the fastest way to improve?

Justify every digit you place. Ten puzzles with justification beat a hundred solved by feel.