Techniques / Subsets

Naked Pair

Also called Conjugate Pair (loose usage), Disjoint Subset of size 2, Naked Double.

New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.

What it means

Two squares in the same group both hold only the same two digits. Those two digits fill those two squares, so rub them out of every other square in the group.

The exact rule, for stronger players

The rule, stated exactly: For a house H, if two cells of H have identical candidate sets of cardinality two, those two digits may be eliminated from every other cell of H.

What it removes: Remove both digits from all cells of H outside the pair.

Why it works: The two cells together must hold both digits, in some order. Every digit occupies exactly one cell per house, so both digits are consumed by these two cells and are unavailable elsewhere in H.

Worked examples

These come from real Proven Sudoku boards. Nobody drew them by hand to make the pattern look neat. Each one is checked first, so the board is one you could really meet, the pattern is really there, and every digit it rules out is really wrong.

Sudoku grid showing Naked Pair. r1c2, r1c3 in r1 hold only 2, 7 between them, so those two digits fill those cells and appear nowhere else in r1. — r1c2, r1c3 in r1 hold only 2, 7 between them, so those two digits fill those cells and appear nowhere else in r1.

Sudoku grid showing Naked Pair. r2c2, r2c5 in r2 hold only 3, 7 between them, so those two digits fill those cells and appear nowhere else in r2. — r2c2, r2c5 in r2 hold only 3, 7 between them, so those two digits fill those cells and appear nowhere else in r2.

Learn these first

Naked SingleA square has only one digit left that fits.

Related subsets

Naked QuadFour squares in one group share the same four digits between them.
Naked Subset (general form)Find some squares in one row, column or box.
Naked TripleThree squares in one group share the same three digits between them.
Hidden PairTwo digits in one group can only go in the same two squares.
Hidden QuadFour digits in a group can only go in the same four squares.

How often does it come up?

Our rough estimate: common at medium difficulty and above.

Play today's puzzle or read how difficulty is graded.