Almost every explanation of Sudoku starts by telling you the rules and then abandons you in front of a grid. The rules take fifteen seconds; knowing what to actually do takes longer, and it is the part most guides skip. This article is the missing part. By the end you will be able to open any easy or medium puzzle and finish it without guessing, using two techniques and one habit.
The rule, and what follows from it
A Sudoku grid is nine rows by nine columns, subdivided into nine three-by-three boxes. Some cells start filled — these are the givens, and they never change. The one rule is: every row, every column, and every box must contain each of the digits 1 through 9 exactly once. That is the whole game. There is no arithmetic in Sudoku; the digits are just nine distinguishable symbols and could as easily be nine colours.
The rule has a consequence more useful than the rule itself. Because a digit appears exactly once per unit, placing a digit anywhere forbids it in twenty other cells: the other eight in its row, the other eight in its column, and the four remaining cells of its box that the row and column have not already covered. Sudoku is not a game of finding where digits go. It is a game of finding where they cannot go, until only one place is left. Everything below is a way of organising that search.
One more guarantee worth knowing: a properly constructed puzzle has exactly one solution, reachable by pure logic. If you ever find yourself flipping a mental coin between two options, you have not hit a hard puzzle — you have missed something, or the puzzle is faulty. Every puzzle on this site is machine-verified for a unique solution before it is published.
Technique one: the Naked Single
Pick any empty cell. Look along its row and note every digit already there. Do the same for its column, then its box. Cross all of those off the list 1–9. Whatever survives is what could legally go in that cell. When exactly one digit survives, you have a Naked Single, and you can write it in with complete confidence — not because it looks right, but because the other eight digits are provably impossible.
Naked Singles are most common in crowded areas of the grid. A cell sitting in a row with six digits already placed, inside a box with five, has very little room left. So do not start at cell one and read left to right. Start wherever the grid is most full.
The habit that doubles your speed here is simple: after writing any digit, immediately look at the cells around it, in the same row, column and box. You have just eliminated a possibility from twenty cells; if any of them was down to two candidates, it is now down to one. Beginners tend to place a digit and then restart their scan from the top-left corner, which discards exactly the information they just created. Follow the chain instead. On easy puzzles a single placement can cascade into fifteen more without you ever needing another technique.
Technique two: the Hidden Single
Eventually the cascade stops. No cell is down to one candidate, and the puzzle looks stuck. It is not — you have just been asking the wrong question. The Naked Single asks what can go in this cell? The Hidden Single asks the reverse: where can this digit go in this unit?
Take a digit, say 7. Look at a box that does not contain a 7 yet. Now look at the rows and columns passing through that box: any of them that already contain a 7 forbid it throughout their length. Mentally strike those lines through the box. Sometimes only one empty cell in the box survives — and that cell must be the 7, even if three or four other digits could also legally fit there. The 7 has nowhere else to go in that box, and the box needs one.
This is the technique that trips people up, because the target cell does not look special. It is not down to one option; it may have five. The single is hidden in the sense that the evidence lives outside the cell, in the absence of alternatives across the rest of the unit. Getting comfortable with this shift — reasoning about a digit's options rather than a cell's — is the single biggest step in a beginner's development.
The systematic version of this scan is called cross-hatching, and it is worth doing in order: take digit 1, sweep every box, then digit 2, and so on. Digits that already appear six or seven times on the grid are the most productive, because they project the most lines. A full pass of cross-hatching, done properly, will finish a large share of newspaper puzzles by itself. The scanning guide covers the mechanics in more detail.
A worked sequence
Rather than abstract advice, here is the loop an experienced solver actually runs, in order, on an easy grid:
- Cross-hatch each digit 1–9 through every box, placing any Hidden Singles you find. This is usually where the first ten or fifteen placements come from.
- Every time you place a digit, check its row, column and box for a Naked Single. Follow any cascade to exhaustion before returning to the cross-hatch.
- When cross-hatching by box stops producing, cross-hatch by row and by column instead. The same digit that had three homes in a box may have only one in a row.
- When that stops producing too, and only then, start writing pencil marks.
Step four is deliberately last. Filling in candidate marks everywhere is slow, and on an easy puzzle it is wasted work — you will place most of the grid before you would have finished annotating it. The pencil-marks guide explains when marking up genuinely pays for itself and how to keep it from becoming a chore.
When you get properly stuck
On a medium or hard puzzle, singles will run out while the grid is still half empty. That is by design: the puzzle has been built to require something more. At that point the next rung is almost always one of two things.
The first is Omission, also called locked candidates. If within one box a digit can only appear in cells that all lie in the same row, then that digit is somewhere in that row — so it can be eliminated from the rest of that row outside the box, even though you have not placed anything. This is the highest-value technique per unit of effort in all of Sudoku, and it is the rung most self-taught solvers are missing.
The second is the Naked Pair: two cells in the same unit showing the same two candidates. Those two digits must fill those two cells in some order, so both can be struck from every other cell in the unit. This is the first technique that gives you eliminations without a placement, which feels unproductive the first few times and is in fact how all harder Sudoku works.
Both are covered properly on their own pages, with live demonstrations and practice puzzles. The learning-order guide sets out the full ladder beyond them, up through X-Wing and Swordfish.
Four habits worth building early
- Never guess. A guess that happens to be right is worse than a guess that is wrong, because you cannot tell which one it was, and twenty placements later a contradiction appears with no way to trace it. If you cannot justify a digit, do not write it. The board on this site is built around this principle — you eliminate candidates you can defend, and cells resolve themselves once one candidate remains.
- Work the fullest units first. Constraint concentrates. A row with seven givens will yield before a row with two, every single time.
- Re-scan after every placement. Almost every beginner stall is not a hard puzzle but an un-followed cascade.
- When stuck, change the question. If “what fits in this cell?” has stopped working, switch to “where does this digit go in this unit?” The two questions surface different information from the same grid, and alternating between them is most of practical solving.
Where to go next
The fastest way to consolidate all of this is deliberate repetition on puzzles that are guaranteed to contain the pattern you are practising, rather than random puzzles that might. Start with the curated Naked Single practice set, then Hidden Singles, and stay there until an easy grid falls without pencil marks at all. Fluency in singles is not a beginner phase you graduate out of — it is the substrate every advanced technique cashes out into, and time invested there pays off at every level above.
When singles are automatic, work through the worked walkthroughs, which show real boards before and after each technique fires, and pick up the glossary for any term you meet that this article did not cover.