Naked Pairs Sudoku: How to Spot Them and Clear the Grid

A naked pair in sudoku is two cells in the same unit that each hold exactly the same two candidates and nothing else. Between them those two cells will use up both digits, so every other cell in that unit can drop both — often several candidates at once, from a pattern you can spot in a couple of seconds.

Naked pairs sudoku solving is the cheapest way to break a stalled grid after singles and locked candidates. There is no chain to trace and no rectangle to verify. Two identical two-candidate cells sitting in one row, one column or one box, and the deduction is already done.

What follows: the exact conditions, three worked examples with candidate grids before and after, the double-unit bonus most solvers miss, and how a naked pair differs from a hidden pair.

What counts as a naked pair

Two cells form a naked pair when they share a unit, each has exactly two candidates, and their two candidate lists are identical.

All three conditions are strict.

The word "naked" means the two candidates are sitting in plain view, with nothing else in the cell hiding them. That contrasts with a hidden pair, where the same two digits are buried among other candidates — covered further down.

The reasoning takes one line. R4C1 is a 3 or a 7. R4C3 is a 3 or a 7. They are in the same row, so they cannot both be the same digit. Between them they consume the 3 and the 7 for that row, in one order or the other. Row 4's 3 and row 4's 7 are therefore spoken for, and no other cell in row 4 may claim either.

Notice you never learn which cell gets which digit. You do not need to. The elimination holds under both arrangements, which is what makes this a proof rather than a guess.

Worked example: a naked pair in a row

Here is a naked pair doing real damage — three cells cleaned, one digit placed, and a second pair created out of the wreckage.

Row 4 on a stalled grid. R4C4, R4C6, R4C8 and R4C9 are already solved as 5, 2, 6 and 4.

Before — row 4:

R4C1 and R4C3 both read exactly {3, 7}. Same row, two candidates each, identical lists — a naked pair.

Strip 3 and 7 from every other unsolved cell in row 4.

After:

R4C5 is now an 8. Worth noting that this was not findable as a hidden single beforehand: the digit 8 had two homes in row 4, at R4C2 and R4C5, so scanning would have told you nothing. The naked pair is what closed it.

The cascade continues. Placing 8 at R4C5 removes 8 from R4C2, which becomes {1, 9}. And R4C7 already reads {1, 9}.

A second naked pair, born from the first. Row 4 now resolves cleanly: {3,7} at C1 and C3, an 8 at C5, and {1,9} at C2 and C7 — five cells, five digits, all accounted for. This is why the standing instruction after any elimination is to re-read the unit you just changed.

The double-unit bonus almost everyone misses

When both cells of a naked pair sit in the same box as well as the same line, the pair clears two units at once — and the box eliminations are usually the more valuable half.

Look again at R4C1 and R4C3. They share row 4. They also both sit inside box 4, the block covering rows 4–6 and columns 1–3. The pair is locked into that box just as firmly as it is locked into the row.

Box 4 before:

Box 4 after — 3 and 7 stripped from rows 5 and 6 as well:

Three more candidates gone, and R5C1 drops to {4, 6} — a new bi-value cell that feeds the wing techniques later in the ladder.

The rule to memorize: check whether the pair shares a box, and if it does, clear the box too. Two cells in the same row share a box whenever they sit in the same three-column span (C1–C3, C4–C6 or C7–C9). Two cells in the same column share a box when they sit in the same three-row band.

When they do not share a box — say a pair at R1C3 and R7C3, both reading {4,9} — the pair still works perfectly on column 3, clearing 4 and 9 from the seven other cells in that column. It just does not get the bonus.

A naked pair inside a box only

A naked pair does not need a shared row or column at all. Two cells in the same 3×3 box with identical two-candidate lists clear that box, even if they share nothing else.

Box 2 covers rows 1–3 and columns 4–6. Suppose R1C4 reads {2, 8} and R3C6 reads {2, 8}. Different row, different column, same box.

Between them they take the box's 2 and the box's 8. Every other cell in box 2 — R1C5, R1C6, R2C4, R2C5, R2C6, R3C4, R3C5 — loses both digits, if it had them.

This variety hides better than the row version, because the two cells are not lined up for your eye to catch. When you sweep for pairs, sweep boxes as their own pass rather than assuming the row and column passes will cover everything.

Naked pair versus hidden pair

A naked pair is two cells holding only two digits. A hidden pair is two digits that can only go in two cells — the same underlying situation, seen from the opposite direction, and it needs to be converted before you can use it.

Say row 9 contains these candidate lists, and you check where the digits 3 and 6 can go:

The digit 3 has exactly two homes in row 9: R9C2 and R9C5. The digit 6 has exactly the same two homes. So those two cells must be the 3 and the 6 in some order, and everything else in them is impossible.

Strip them down: R9C2 becomes {3, 6}, R9C5 becomes {3, 6}. Four candidates removed from inside the two cells rather than from the rest of the row.

And now you have a naked pair. That is always the relationship — a hidden pair, once reduced, is a naked pair. The practical difference is where the eliminations land:

Most solvers find naked pairs constantly and hidden pairs almost never, purely because naked ones are visually obvious. If a grid is stalled and the naked sweep found nothing, the digit-by-digit hidden sweep is the next thing to try.

Naked triples, and the trap inside them

A naked triple is three cells in one unit whose candidates, pooled together, total exactly three digits — and crucially, no cell has to contain all three.

This is where solvers get caught. Row 5 has:

• R5C7 = {2, 5}
• R5C8 = {5, 9}
• R5C9 = {2, 9}

Pool them: {2, 5, 9}. Three cells, three digits. Those three cells will use up 2, 5 and 9 between them, so all three digits come out of every other cell in row 5.

None of the three cells reads {2,5,9}, and none needs to. The valid shapes for a naked triple are any mixture of {2,5,9}, {2,5}, {5,9} and {2,9} across the three cells, as long as the union is exactly three digits and every cell's list is a subset of it. The "all three cells must show all three digits" belief costs people most of their triples.

Naked quads work the same way with four cells and four digits, but they are rare enough and slow enough to check that they are usually not worth hunting deliberately.

How to find naked pairs sudoku patterns fast

Scan for bi-value cells first, because every naked pair is made of two of them.

1. Complete the candidate grid. Every unsolved cell, checked against its row, column and box. Naked pairs read off stale pencil marks are not naked pairs.

1. Circle every cell with exactly two candidates. On a stalled hard grid there are usually between eight and twenty. This is the entire search space for pairs.

1. Group the circled cells by their candidate list. Write 37: R4C1, R4C3, R8C1 and so on down the margin. Any list that appears twice is a candidate pair — you only need to check whether the two cells share a unit.

1. Check row, column, and box for each match. Same row? Same column? Same three-by-three block? Any one of those is enough.

1. Apply, then check the shared box separately. If both cells sit in the same box as well as the same line, clear both units.

1. Go back to singles. Every naked pair elimination can produce one.

Grouping by candidate list in step 3 is what makes this fast. Comparing every bi-value cell against every other one is roughly a hundred comparisons; sorting them into groups is one pass.

Where naked pairs fit in the solving ladder

Naked pairs sudoku work sits just above locked candidates and just below the single-digit patterns, and together those first three techniques finish nearly every puzzle rated hard.

The next technique to learn is the X-Wing. It is the first pattern that works on a single digit spread across four cells rather than on candidate lists inside one unit, and it is the gateway to swordfish and the wings. If you have not yet met locked candidates, go there first — it is easier than this page and fires more often.

For practice grids, our free puzzle maker produces unlimited classic sudoku at easy, medium and hard, prints one to six per page with an answer key, and checks that every puzzle has exactly one solution.

Frequently asked questions

What is a naked pair in sudoku?

A naked pair is two cells in the same row, column or box that each have exactly two candidates left, and those two candidates are identical. Because the two cells will use up both digits between them, no other cell in that shared unit can contain either digit. You do not need to know which cell takes which value — the elimination is valid under both arrangements.

Do naked pairs have to be next to each other?

No. They only have to share a unit. R4C1 and R4C9 sitting at opposite ends of row 4 form a perfectly good naked pair. Adjacency helps you notice them, which is why pairs inside a single box are the easiest to see and pairs at the far ends of a long row are the easiest to walk past.

What is the difference between a naked pair and a hidden pair?

A naked pair is two cells holding only two candidates; you erase those digits from the rest of the unit. A hidden pair is two digits whose only homes in a unit are the same two cells; you erase every other candidate from inside those two cells. Reducing a hidden pair turns it into a naked pair, so they describe the same situation from opposite directions.

Can the naked pairs sudoku technique clear two units at once?

Yes, and it is the most commonly missed part of the technique. If both cells of the pair sit in the same box as well as the same row or column, the pair is locked into both units and you can erase the digits from the rest of the box too. That happens whenever the two cells fall inside the same three-column span or three-row band.

Does a naked pair ever place a number directly?

Not on its own — it only removes candidates. But the removals frequently reduce another cell to a single candidate, or leave a digit with only one home in a unit. In the worked example above, the pair at R4C1 and R4C3 placed an 8 at R4C5 as a second-order effect and then created a fresh pair. Always return to singles after applying one.

Are naked pairs enough to solve hard sudoku?

Often, yes. Singles, locked candidates and naked pairs together will finish the large majority of puzzles rated hard by mainstream generators. Expert and evil grids are specifically constructed to survive all three, which is where the single-digit patterns like the X-Wing and the wings become necessary.