Obvious Pairs: When Two Cells Lock Together

Obvious Pairs, also called Naked Pairs, is your first foray into candidate elimination — techniques that don't directly place a number but instead remove candidates from other cells, setting up future placements. The idea is elegant: if two cells within the same row, column, or 3×3 box contain the exact same two candidate numbers (and no other candidates), those two numbers are "locked" into those two cells. No other cell in that unit can contain those two numbers, so you can safely eliminate them everywhere else.

How Obvious Pairs Work

The mechanic is straightforward once you see it:

• Step 1: While scanning a unit (row, column, or box), look for two cells that each contain exactly the same two candidates — for example, both cells show 7 and no other possibilities.
• Step 2: Recognize that these two cells form a locked pair. One must be 3 and the other must be 7. You don't yet know which is which, but you know for certain that 3 and 7 will occupy these two cells.
• Step 3: Eliminate 3 and 7 as candidates from every other cell in that same unit. Those two numbers are spoken for — they cannot appear anywhere else in the row, column, or box.

Why This Works

The logic is ironclad and worth understanding deeply because it underlies all "naked subset" techniques (pairs, triples, quads). In Sudoku, every number 1-9 must appear exactly once in every unit. If two cells both have 7 as their only candidates, then those two cells collectively must consume both the 3 and the 7 for that unit. Even though you don't know which cell gets 3 and which gets 7, you know with 100% certainty that no other cell in the unit can receive either digit. The pair has claimed exclusive rights.

Concrete Example

Imagine row 5 has the following candidate sets, moving left to right:

• R5C1: 9
• R5C2: 3, 7
• R5C3: 8
• R5C4: 3
• R5C5: 3, 7
• R5C6: 7
• R5C7: 9
• R5C8: 9
• R5C9: 6

Cells R5C2 and R5C5 both contain exactly 7. They are an Obvious Pair. This means we can eliminate 3 and 7 from every other cell in row 5 — removing 3 from R5C1 and R5C4, and removing 7 from R5C6 and R5C8. After elimination, R5C1 becomes 9, R5C4 becomes 6, R5C6 becomes 8, and R5C8 becomes 9. Notice that we haven't placed a single number yet — but we've dramatically simplified the candidate landscape, and new Obvious Singles may now emerge.

Spotting Obvious Pairs

Obvious Pairs are easiest to spot when you have all candidates written out — either on paper in small notation or using the automatic candidate mode in a digital Sudoku app. Scan each row, each column, and each box. Look for cells that list exactly two candidates. If you find a second cell in the same unit with the exact same two-candidate set, you've found a Naked Pair. The consistency of the pair (both cells having exactly the same two numbers and no others) is what makes them "naked" — there's nothing hiding behind other candidates.

Obvious Pairs vs. Hidden Pairs

It's important not to confuse Obvious Pairs with Hidden Pairs. Obvious Pairs are "naked" because the two target cells show only those two candidates and nothing else. Hidden Pairs are the reverse: the two numbers appear only in two cells within a unit, but those cells may also contain many other candidates. In Hidden Pairs, you eliminate the extra candidates from those two cells. In Obvious Pairs, you eliminate the pair numbers from other cells. Both are valuable; Naked Pairs are easier to spot.

When to Use Obvious Pairs

This technique becomes essential on Medium and Hard puzzles. You'll frequently encounter situations where Obvious Singles run dry but the board is dotted with two-candidate cells. Methodically scanning each unit for matching pairs is often the breakthrough that unlocks the puzzle. On Expert and Extreme puzzles, Obvious Pairs are often combined with Obvious Triples and Hidden Singles to gradually chip away at the candidate space until placements appear.