7 Sudoku Techniques and the Order to Learn Them

Staring at a sudoku grid does not solve it. Progress comes from a fixed set of patterns — techniques — that you learn in a particular order and apply in that order.

This article lists seven techniques, arranged from easiest to hardest, and says exactly where on the grid to look for each one. It also covers what to check when you get stuck, which is usually not a missing technique at all. A free sudoku you can play in the browser is embedded at the end so you can practise straight away.

Sudoku has only three rules

Every row, every column and every 3×3 box must contain the digits 1 through 9 exactly once. That is the whole game.

A 9×9 grid contains nine rows, nine columns, and nine boxes marked off by heavy lines. In sudoku terminology these three kinds of group are called units.

▼The three rules

① Each row holds 1–9 once each

② Each column holds 1–9 once each

③ Each 3×3 box holds 1–9 once each

Every cell belongs to three units at the same time — a row, a column and a box. Every technique below is a way of using those overlapping units to narrow down what can go where. Three rules produce hard puzzles precisely because the three units interfere with each other.

Candidates come first

One term is needed before the techniques. The digits that could still legally go in a given cell are that cell’s candidates.

If a cell’s row already holds 1, 2 and 3, its column holds 4 and 5, and its box holds 6, then its candidates are 7, 8 and 9. Solving sudoku is the process of removing candidates. The advanced techniques do not place digits at all; they eliminate possibilities.

The order to learn them in

Learn these top to bottom. The last three only become useful once the first four are exhausted.

#	Technique	What it does	Needed from
1	Naked single	Places a digit	Easy
2	Hidden single	Places a digit	Easy
3	Naked pair	Removes candidates	Medium
4	Locked candidates	Removes candidates	Medium
5	Hidden pair	Removes candidates	Hard
6	Naked triple	Removes candidates	Hard
7	X-Wing	Removes candidates	Expert

Techniques 1 and 2 alone will finish any easy puzzle. Being unable to solve a hard puzzle is not a matter of intelligence — it means you have not learned techniques 3 onwards.

Technique 1: naked single

Pick one cell, cross off every digit already present in its row, column and box, and if a single digit survives, that is the answer.

This is the foundation. Look at a cell, eliminate everything its three units forbid, and see what remains. One candidate left means the cell is solved.

▼Where to look

▶ Start with the rows, columns and boxes that are already well filled

▶ Watch intersections. A cell where a full row meets a full column has very few candidates

▶ After placing a digit, immediately re-check its surroundings. These often chain

The trick is not to scan the whole grid. Target a row with seven digits already in it, or a box with eight, and naked singles appear quickly.

Technique 2: hidden single

Where technique 1 examines a cell, this one examines a digit. If a digit can only go in one cell of a row, it goes there.

The viewpoint flips completely. Suppose a row is missing a 5. Walk its empty cells and rule out the ones where a 5 is blocked by their column or box. If exactly one cell survives, that cell is a 5.

It does not matter how many other candidates that cell still holds. The fact that the row has nowhere else to put a 5 settles it. This is the step beginners most often fail to see.

▼Where hidden singles hide

▶ Choose a digit that already appears many times on the grid — one with seven placements, say

▶ Trace the rows and columns holding it, then look at boxes that still lack it

▶ Scanning box by box is the easiest way to spot them

With practice this becomes digit-by-digit scanning: take 1 through 9 in turn and find each digit’s possible boxes. It is faster than working cell by cell and misses less.

Technique 3: naked pair

If two cells in the same unit hold exactly the same two candidates, those two digits can be removed from every other cell in that unit.

Say a row contains one cell with candidates {3, 7} and another with candidates {3, 7}. Between them, those two cells will take one 3 and one 7. Which goes where is unknown, but the row’s 3 and 7 are consumed by this pair.

Therefore 3 and 7 can be struck from every other cell in that row. No cell is solved directly, but the reduced candidates often trigger techniques 1 and 2 elsewhere.

Everything from here on only removes candidates and never places a digit directly. That is why these techniques are unusable without written candidates. Getting stuck on hard puzzles while working in pen means you have reached this stage.

Technique 4: locked candidates

If a digit’s candidates within a box all fall on one row or column, that digit can be removed from the rest of that row or column.

Put another way: suppose in the top-left box, the digit 4 can only go in two of the three cells along the top row of that box. The 4 has to land somewhere in the box, so the 4 must be on that top row.

Which means the cells of the top-middle and top-right boxes on that same row cannot hold a 4, and it can be eliminated there.

▼Two directions of the same idea

▶ Box to line: candidates line up within a box → remove from other boxes along that line

▶ Line to box: candidates in a row all fall inside one box → remove from the box’s other rows

The two directions are the same reasoning reversed. Once you can say “this digit must be inside this region,” everything outside the region can be cleared.

Technique 5: hidden pair

If two digits in a unit can each only go in the same two cells, every other candidate in those two cells can be removed.

This is technique 3 inverted. Suppose in a row, the digit 2 can only go in cells A or B, and the digit 6 can also only go in A or B. Then 2 and 6 occupy A and B between them.

So any other candidates sitting in A and B — 1, 4, 9 or whatever else — can all be struck out. It is called “hidden” because A and B start out with many candidates, so the pair is not visible as a pair.

Technique 3 asks you to look for cells with few candidates. Technique 5 asks you to look for digits with few available cells. The search procedure is completely different, so you have to consciously switch modes.

Technique 6: naked triple

If three cells in a unit hold candidates that together make exactly three distinct digits, those three digits can be removed from the rest of the unit.

It is a naked pair extended to three, with one catch. The three cells do not each need three candidates.

The combination {2, 5, 8} / {2, 5} / {5, 8} qualifies. Their union is the three digits {2, 5, 8}, and three digits fit exactly into three cells. This incomplete form is easy to miss, so get into the habit of counting the union of candidates rather than looking for three matching triples.

Technique 7: X-Wing

If a digit can only go in the same two columns across two different rows, that digit can be removed from those two columns in every other row.

This is the only technique here that crosses units. The four positions form the corners of a rectangle, which is where the name comes from.

Concretely: in row 2, the digit 9 can only go in columns 3 and 7. In row 6, the digit 9 can also only go in columns 3 and 7. The 9s must then occupy either “row 2 column 3 and row 6 column 7” or “row 2 column 7 and row 6 column 3”. Either way, columns 3 and 7 have their 9s used up by rows 2 and 6.

So 9 can be removed from columns 3 and 7 in all other rows. The same works with rows and columns swapped.

X-Wing only appears in expert puzzles, but by this point the shared logic should be clear. Whenever you can say “this digit must be somewhere inside this region,” everything outside that region can be eliminated. All seven techniques reduce to that one sentence.

What to check when you are stuck

Before hunting for a harder technique, doubt your candidate marks. Most dead ends are bookkeeping errors, not missing knowledge.

▼Work down this list

① Look around the cell you solved most recently. Did you clear that digit from its units?

② Find digits that are only placed two or three times so far. Hidden singles are waiting there

③ Find units with only two or three empty cells. These almost always resolve

④ Collect every cell with exactly two candidates. Naked pairs hide among them

⑤ Only now go looking for hidden pairs and X-Wings

Step one is the step people skip. Every time you place a digit, remove it from the candidates of its row, its column and its box. Skip that cleanup and your written candidates drift away from reality, which stops correct techniques from firing.

If you find a contradiction — the same digit twice in a row, say — do not try to trace it backwards. Rewinding to the last placement you are confident about is faster.

Practising with a real grid

Reading about techniques does not install them. Get techniques 1 and 2 down to reflex on easy puzzles, then raise the difficulty — the slow-looking route is the fast one.

The free sudoku published on this blog runs entirely in the browser with no sign-up and no install. It was built with technique practice in mind.

▼Features that support practice

▶ Pencil marks: write candidates into each cell. Techniques 3 and up are unusable without them

▶ Hint: reveals a single cell, so you can see the answer and work out why afterwards

▶ Undo: recover from a misplaced digit

▶ Auto-save: close the tab and resume later

▶ 4×4 mode: good for understanding how techniques 1 and 2 work

There are four difficulty levels. On the 9×9 grid the number of empty cells is 38 for easy, 48 for normal, 56 for hard and 60 for expert. Fewer starting clues means fewer footholds, so easy suits techniques 1–2, normal suits 3–4, and hard or expert is where 5–7 earn their place.

The 4×4 grid uses 6, 8, 10 and 11 empty cells with 2×2 boxes and only the digits 1–4. When you want to check that you have understood the logic of a technique, 4×4 gives you far more repetitions per minute than 9×9.

Summary

Sudoku techniques split into two that place digits and five that remove candidates. The first two — naked single and hidden single — are enough for any easy puzzle.

Hard puzzles stop you because you do not know the other five. Naked pair, locked candidates, hidden pair, naked triple and X-Wing are all restatements of the same idea: this digit must land somewhere inside this region, so it can be cleared everywhere outside it. Carrying that sentence around is more useful than memorising seven shapes.

And when you stall, suspect your candidate marks first. Confirm the cleanup after your last placement before you start hunting for advanced patterns. That habit alone eliminates most unsolvable-feeling puzzles.

Technique names vary between books and websites — naked pairs are sometimes called conjugate pairs, and X-Wing appears under other names too. The names used here are the ones most commonly seen in English sudoku literature.