Obvious Pairs

Two cells. Two digits. Zero doubt.

Obvious Pairs — also called Naked Pairs — is an elimination technique that works on two cells at once instead of one. It occurs when exactly two cells in the same row, column, or 3×3 box have notes containing the same two candidate digits and nothing else.

Because those two cells hold only two possible digits between them, and Sudoku won't repeat a digit in a region, the two digits must be split between them — one cell gets one digit, the other gets the second. You don't yet know which cell gets which, but you know with certainty that neither digit can appear anywhere else in that shared region. Every other cell in the row, column, or box that lists either digit as a candidate can have it safely removed. That elimination often narrows another cell down to a single remaining candidate, exposing an obvious single that wasn't visible before the pair was spotted.

How It Works

If two cells in the same region (box, row, or column) have notes {A, B} and {A, B}, then one of them must hold A and the other must hold B. You do not yet know which is which — but you know for certain that A and B will not appear in any other cell in that region.

  1. Find two cells in the same region whose notes are identical and contain exactly two digits.
  2. Eliminate both digits from the notes of every other cell in that shared region.
  3. Look for naked singles that emerge from this elimination.

Example

Below board presents an example of an obvious pair on digits 2 and 5, sitting in two cells of the same row.

the obvious pair {2, 5}
eliminated by the pair

Two cells in this row hold nothing but 2 and 5. Between them, they must take both digits — one cell gets 2, the other gets 5. It doesn't matter which. What matters is that 2 and 5 are now spoken for in this row, so every other cell has to give them up. Three cells feel it:

  • The {2, 6} cell loses its 2. The pair has already claimed the row's only homes for 2, so this cell can no longer be 2. Its 6 is left standing alone.
  • The {5, 8} cell loses its 5. The same holds for the pair's other digit: 5 is taken, so it is struck here, leaving 8 by itself.
  • The {2, 4, 5} cell loses both 2 and 5. It happened to list both pair digits, and both are now off-limits, so both fall at once — leaving 4 as a naked single.

The pair does not directly tell you which cell gets which digit. Its value is in the elimination it forces upon the surrounding cells. In this example, the elimination produced 3 naked singles.

On Evil Boards

Obvious pairs are one of the most used techniques even on the most evil boards. Unlike the advanced patterns reserved for late-game stalemates, this one keeps paying off from the very first notes you write to the very last cell you fill. Scanning for obvious pairs first is rarely a wasted effort. If a region shows no obvious pair, check it for hidden pairs and pointing pairs.