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Sudoku Naked Pairs: Two Cells, Two Digits

A naked pair is two cells in the same row, column or box whose notes are the same two digits, and nothing else. Between them, those two cells must take both digits, one each. You don’t know which way round yet, but no other cell in that row, column or box can have either digit, so cross them out.

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This is the fourth of the Sudoku techniques. It needs full notes, at least in the row, column or box you’re looking at.

The rule

  1. In one row, column or box, find two cells whose notes are exactly the same two digits.
  2. Cross both digits out of every other cell in that row, column or box.
Naked pair: 7 and 9 in row 4 Row 4 with full notes. Columns 3 and 8 can each only be 7 or 9, so between them they take both. The 7s and 9s in the row's other cells are ruled out, which leaves column 2 with only 6. 6 7 9 7 9 1 2 9 1 2 3 6 7 9 7 9 2 3 9 3 1 6 5 8 5 9 8 4 7 8 3 2 7 1 6 3 5 1 1 9 8 2 5 7 6 7 4 3 7 2 1 6 6 1 3 5 4 8 8 6 6 5 1
Row 4: columns 3 and 8 are both 7 or 9, so the other 7s and 9s in the row go, leaving column 2 with only 6.

The pair itself doesn’t place anything. Here it leaves column 2 with a single note, 6, and gives column 2’s 7 only one place, both of which place digits straight away.

In a real puzzle

In the Hard puzzle every technique page follows, column 9 has a naked pair just after the box/line reduction step:

Naked pair in the Hard puzzle: 3 and 4 in column 9 Column 9 with full notes. Rows 6 and 9 can each only be 3 or 4, so the 3s and 4s in rows 3, 4 and 7 are ruled out. 1 7 8 9 3 4 7 8 9 1 4 7 9 3 4 4 7 9 3 4 3 5 4 2 7 2 3 5 2 1 3 5 9 2 2 9 7 8 8 1 8 6 7 6 8 1 9 2 3 5 1 9
Column 9: rows 6 and 9 are both 3 or 4, so the 3s and 4s in rows 3, 4 and 7 go.

Column 9’s notes read: row 1 is 1, 7, 8 or 9; row 3 is 3, 4, 7, 8 or 9; row 4 is 1, 4, 7 or 9; row 6 is 3 or 4; row 7 is 4, 7 or 9; and row 9 is 3 or 4. Rows 6 and 9 are the pair. Row 7 would also have had a 3, but the box/line reduction just ruled it out. Without that step, rows 6 and 9 would still be a pair, but there would be one more 3 to cross out.

Crossing out the pair’s digits takes 3 and 4 out of row 3, 4 out of row 4 and 4 out of row 7. Nothing is placed yet. The next step, a hidden pair, is what finally sets the digits moving again.

How often you’ll need them

On PeerPuzzles, 37 of the 50 Hard levels need a naked pair. Medium and Easy levels never do: they’re built without pairs. So when a Hard level stalls with full notes on the grid, a pair is one of the first things to look for.

Common slips

  • Cells that don’t share a row, column or box. Two cells with the same two notes in different rows, columns and boxes tell you nothing. See mistake 6.
  • A missing note. One note left out can make a fake pair, and acting on it rubs out a right answer. See mistake 4.
  • Crossing out in the wrong place. Only cross out in the row, column or box the pair shares. If the two cells share both a row and a box, you can cross out in both.

Next steps

Questions

Do both cells need exactly the same two notes?

Yes, for a pair. Each cell must have those two digits and nothing else. A cell with a third note can’t be part of a naked pair, though it might be part of a naked triple.

What's a naked triple?

Three cells in one row, column or box whose notes, between them, contain only three digits. Not every cell needs all three: 1 and 2, 2 and 3, and 1 and 3 is a triple. The three digits can then be crossed out of the rest of that row, column or box.

Can the two cells be in different boxes?

Yes, as long as they share a row or a column. What matters is that they’re both in the same row, column or box, and you only cross out digits in that one.