sudokly
Intermediate technique

Naked Pairs

A naked pair is two cells in the same row, column or 3x3 box that contain exactly the same two candidate digits. Those two digits must occupy those two cells, so they can be eliminated from every other cell in the unit.
2 62 6

Naked pairs are the first technique that does not place a digit. They remove candidates instead, and those removals nearly always cascade into a placement somewhere else in the unit.

How it works

A naked pair is two cells in the same row, column or 3x3 box whose candidate sets are exactly the same two digits. Nothing more, nothing less. If r1c3 holds {2, 7} and r1c7 also holds exactly {2, 7}, the digits 2 and 7 must occupy those two cells in some order.

Because 2 and 7 are committed to the pair, neither digit can appear anywhere else in the unit. Every other cell in the row can have 2 and 7 struck off its candidate list.

ROW WITH A NAKED PAIR {2, 7}3 5 92 73 5 85 91 83 92 75 8 91 52 and 7 are locked into the two highlighted cells. erase them from the rest of the row
Two cells share {2, 7}. Those two digits are locked there, so they can be eliminated from every other cell in the row.

When to look for it

Right after laying down pencil marks. Pairs are most visible in units that are already half-placed, where each candidate set is short. Walk every row, every column and every box once and check whether any two cells carry the same two-digit set.

On harder puzzles you will scan again after every batch of placements. New digits prune candidates, and a cell that held three options yesterday may be a pair candidate today.

Step-by-step example

  1. Take a row with eight or nine empty cells. Mark all candidates.
  2. Look for two cells whose candidate set is exactly {A, B} with no extras. r1c3 has {2, 7} and r1c7 has {2, 7}.
  3. Confirm both cells share the row (or column, or box).
  4. For every other empty cell in that unit, erase the digits 2 and 7 from its candidate list.
  5. Re-scan the row for newly created singles. A cell that held {2, 5, 7} now holds {5}. Place the 5.

Naked pair vs hidden pair

Naked pairHidden pair
PatternTwo cells with exactly two candidates eachTwo digits confined to the same two cells
Scan styleCell-firstDigit-first
Eliminations targetOther cells in the unitOther candidates inside the two cells
VisibilityEasy to spot once marks are cleanHidden by extra candidates inside the cells
Two sides of the same coin. Learn both to scan a unit completely.

Tips for spotting it

  • Scan units with the fewest empty cells first; pairs there are easiest to see.
  • If you find a pair but no eliminations follow, the pair was already implicit. Move on.
  • Highlight the two cells with a dot or a tick so you do not lose track when sweeping the unit.
  • After eliminating, re-scan for singles right away. Pairs nearly always feed into a placement.

Common mistakes

  • Treating a near-pair as a real pair. Three candidates breaks the pattern.
  • Forgetting to apply the eliminations. The pair itself does not place anything.
  • Mistaking a pair for a hidden pair. Naked is about the cells; hidden is about the digits.
  • Letting pencil marks drift so the pair never appears.

Practise it

Medium sudoku is full of naked pairs. Mark every empty cell before placing anything and you will usually find one or two pairs immediately. Once those become reflex, move to naked triples and the rest of the pair family.

Related strategies