Sudoku strategy: every technique, in the right order

How to solve Sudoku properly

Every Sudoku technique is an answer to one question: which digit can go where? The techniques get more elaborate, but they never get more complicated than that — they just look at more squares at once.

Solve in this order, always. Move to the next level only when the current one stops producing anything:

1. Scan for hidden singles — a digit with only one home in a unit.
2. Look for naked singles — a square with only one candidate.
3. Pencil mark, then eliminate with pairs and pointing pairs.
4. Apply the named patterns — X-Wing, XY-Wing, and the rest.

Level 1 — Basic: singles and cross-hatching

Cross-hatching (hidden singles)

Take a digit — say 5 — and a box. Cross out every square in the box that shares a row or column with an existing 5. If exactly one square survives, the 5 goes there. Work through all nine digits, then all nine boxes, then start again. On an easy puzzle this alone finishes the grid.

Naked singles

A square where eight different digits already appear in its row, column and box must hold the ninth. These are easiest to spot in crowded regions — which is why you should always work where the grid is fullest.

Work systematically

• By digit — scan all nine boxes for one digit at a time. Best early.
• By unit — take a nearly full row, column or box and ask what is missing. Best later.

Switching between the two when you get stuck is worth more than any clever pattern at this level.

Three habits that prevent errors

1. Never write a digit you have not proved. One wrong entry poisons everything after it.
2. Re-scan the affected units immediately after writing a digit — it usually unlocks another.
3. If you are stuck for a long time, check for a mistake rather than looking for a harder technique.

Level 2 — Intermediate: pairs, pointing and box-line

Naked pairs, triples and quads

If two squares in a unit have the same two candidates, those two digits are used up by those two squares — so they can be removed from every other square in that unit. The same works with three squares sharing three candidates, and four sharing four.

Hidden pairs

The mirror image: if two digits can only appear in the same two squares of a unit, those squares hold those digits and every other candidate in them can be deleted. Hidden pairs are harder to see because the evidence is scattered rather than sitting in one square.

Pointing pairs and box-line reduction

These two are the workhorses of medium puzzles, and they are the same idea seen from both sides:

• Pointing pair — if, inside a box, a digit's only candidates lie in one row, then that digit must be in that row within the box, so it can be eliminated from the rest of the row.
• Box-line reduction — if, along a row, a digit's only candidates lie inside one box, it can be eliminated from the rest of that box.

Pencil marks: mark everything or nothing

Once you start marking, mark every candidate in every empty square. Half-marked grids cause the most common error in Sudoku: trusting a mark you never updated after writing a digit.

Level 3 — Advanced: X-Wing, XY-Wing, chains and uniqueness

X-Wing

The first genuinely advanced pattern, and the gateway to all the rest. If a digit's candidates in two rows are confined to the same two columns, then those four squares form a rectangle, and whichever diagonal is correct, the digit occupies one square in each column — so it can be eliminated from the rest of those two columns.

Swordfish is the same pattern with three rows and three columns; Jellyfish with four. They are rarer and harder to spot, and the logic is identical.

XY-Wing

Three squares with exactly two candidates each: a "pivot" with candidates XY, and two "wings" with XZ and YZ, each seeing the pivot. Whatever the pivot turns out to be, one of the wings must be Z — so Z can be eliminated from any square that sees both wings. It is the simplest chain, and learning it changes how you read a grid.

Colouring and chains

Take a digit whose candidates form a network of pairs. Colour them alternately along each link. Two squares of the same colour in a unit proves that colour is false, which resolves the entire chain at once. Longer techniques — X-Cycles, forcing chains, nets — are elaborations of this.

Uniqueness patterns

Because a proper puzzle has exactly one solution, any arrangement that would allow two solutions must be impossible. The commonest is the Unique Rectangle: four squares in two rows, two columns and two boxes with the same two candidates would be interchangeable, so one of them must hold something else.

Solving faster

• Scan by digit first — it is the highest-yield technique per second spent.
• Do not mark early. Marking a grid takes minutes; scanning often makes it unnecessary.
• Learn to spot pairs by shape, not by reading numbers. Speed solvers work visually.
• Stop and check the moment something feels wrong; a contradiction found early costs seconds, found late costs the puzzle.

Where solvers go wrong

1. Guessing to break a deadlock — it destroys the puzzle and teaches nothing.
2. Partial pencil marks that were never updated.
3. Reaching for X-Wings before exhausting pointing pairs, which are far more common.
4. Scanning only the digits you can see and skipping the ones with few clues, which are often the most constrained.
5. Not re-scanning the row, column and box after each entry.
6. Continuing after an error instead of checking when progress mysteriously stops.

Common questions