Advanced sudoku techniques: pointing pairs, naked pairs, and X-wings

Hard and expert grids are not harder because they need smarter guesses. They are harder because the easy techniques—cross-hatching, naked singles, hidden singles—stop being sufficient, and you need the next layer of elimination. Everything below is still pure logic: no guessing, no trial branches, no pencil-mark roulette.

If you have not yet mastered the fundamentals, read sudoku strategies for beginners first. The techniques here assume your candidate lists are accurate, because every one of them depends on notes being correct.

Locked candidates: pointing and claiming

A pointing pair is the most common intermediate technique and the one that unblocks most stuck hard puzzles. If every candidate for a digit inside a box sits in one row, then that digit has nowhere to go in the rest of that row—you can delete it from all the other cells in the row, including cells outside the box.

The mirror version is claiming. If all candidates for a digit within a row are confined to a single box, the digit cannot appear elsewhere in that box. Both are easy to miss because they are stated about a line and a box at the same time, so train yourself to check each box for line alignment before you move on.

Naked pairs and naked triples

Find two cells in the same row, column, or box that have exactly the same two candidates—say {4, 7} and {4, 7}. Those two digits are now committed to those two cells in some order, so a 4 or a 7 can be removed from every other cell in that unit. Two candidates, two cells: everything else in the unit just lost two possibilities.

A naked triple works the same way with three cells sharing a total of three digits, even if the individual cells contain two candidates each. Triples are harder to spot because the cells need not look identical—what matters is that the union of their candidates is only three digits.

Hidden pairs and hidden triples

These are the opposite framing. If two digits appear as candidates nowhere in a unit except in two cells, those two cells are the only possible home for both digits. Everything else in those cells can be erased—whatever third or fourth candidate they carried, it cannot be used, because one of the two locked digits must occupy the cell.

Hidden pairs are most often found in long rows with crowded candidate lists. The signal to look for is a digit that appears in only two cells of a unit you have already examined; do that twice in the same unit and you have your pair.

Box/line reduction

Box/line reduction generalises pointing and claiming into one rule: if a digit can only appear in one box within a row or column, remove it from the rest of that box. Practically, you scan a row, notice that a 5 only fits in the two cells that row shares with box four, and delete 5 from every other cell in box four.

On expert grids this technique does a surprising amount of work, because crowded boxes are exactly where candidate lists get squeezed down to the point that a single line observation collapses several cells at once.

X-wing: the first pattern worth memorising

An X-wing appears when a digit has candidates in exactly two columns of one row, and in exactly two columns of a second row—and those two columns are the same pair. The digit must occupy those four corner cells, two per row, so it can be eliminated from the rest of both columns.

The shape is a rectangle: four cells, two rows, two columns, one digit. It is rare enough that you can afford to check for it deliberately once per stuck puzzle. Start by looking at the digit with the fewest candidate occurrences left on the board—X-wings live among digits that are nearly placed.

A practical order of attack

1. Fill every obvious placement with cross-hatching.
2. Build complete, accurate candidate lists.
3. Sweep for singles, then for locked candidates.
4. Look for naked pairs, then triples.
5. Check for hidden pairs in crowded units.
6. Run box/line reduction along each row and column.
7. Only then consider X-wings or more advanced patterns.

Work the list in that order every time. The techniques are ordered by how often they pay off, and skipping ahead is the usual reason a puzzle feels impossible—you are looking for an X-wing while a naked pair sits three cells away.

Practising on this site

Hard sudoku is where pairs first become necessary; use it to learn locked candidates and naked pairs without pressure. Expert sudoku adds triples, box/line reduction, and the occasional X-wing. Both accept notes, so you can work the full candidate lists these techniques require.

When you want a fixed benchmark to measure progress against, today's daily sudoku is the same grid for everyone, so a solve time is directly comparable with a friend.

Frequently asked questions

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