Naked Pairs, Hidden Pairs & Pointing Pairs: The Intermediate Player's Toolkit
Sudoku a Day Blog ·
You have mastered the basics. Scanning, naked singles, maybe locked candidates. Easy puzzles feel comfortable, but medium puzzles hit a wall that scanning alone cannot break.
That wall has a name: pairs. Specifically, three types of pairs that together handle the vast majority of stuck moments in medium — and even many hard — puzzles. Once you understand naked pairs, hidden pairs, and pointing pairs as a system, medium difficulty unlocks. This guide presents all three together, in the order you should learn them.
Why "Pairs" — and Why Three Types?
In Sudoku, a pair is a situation where two candidates are constrained to exactly two cells within a unit (a row, column, or box). That constraint lets you eliminate candidates elsewhere. Each of the three techniques identifies pairs differently and eliminates candidates in different places.
Think of them as a progression system:
- Pointing pairs — the easiest. A digit locked inside a box that eliminates it from the wider row or column.
- Naked pairs — two cells with only two identical candidates. Eliminates from the rest of the unit.
- Hidden pairs — two candidates hiding in two cells. Eliminates the non-pair candidates from those cells.
Technique 1: Pointing Pairs
Pointing pairs — also called locked candidates — are the most frequently occurring of the three. They appear often enough that every medium puzzle will likely require them at least once.
The concept: Look inside a 3×3 box. Find a digit that appears as a candidate in only two (or three) cells within that box, and those cells all lie in the same row or column. Because that digit must go into one of those cells, you can eliminate it from the rest of that row or column — the part outside the box.
Worked example: In a 3×3 box, the digit 4 can only go in two cells, both in row 5. Row 5 passes through two other boxes. In both of those boxes, row 5 cells that contain 4 as a candidate can have it removed — because if 4 must go somewhere in the first box's row-5 cells, it cannot also appear in row 5 elsewhere.
How to spot them: After scanning each digit globally, zoom into each 3×3 box. Ask: "In this box, which digits appear in only one row or column?" Those are your pointing pair candidates.
Technique 2: Naked Pairs
A naked pair is two cells within the same unit that each contain exactly the same two candidates — no others. Because those two digits must fill those two cells (in some order), no other cell in that unit can contain either digit.
Worked example: In a column, two cells both contain only the candidates {3, 8}. The digit 3 must go into one of them, and 8 into the other. Therefore, every other cell in that column can have 3 and 8 safely removed from their candidates. Sometimes that elimination produces a naked single elsewhere, cascading into more placements.
How to spot them: Scan each unit for cells that contain exactly two candidates. If you find two cells in the same unit with the same two-candidate set, you have a naked pair. Eliminate both digits from all other cells in that unit.
Naked triples follow the same logic: three cells in a unit that together contain exactly three candidates (distributed across the three cells, not necessarily all three in each cell). Eliminate those three digits from all other cells in the unit. Naked triples are harder to spot but worth knowing once pairs feel natural.
Technique 3: Hidden Pairs
Hidden pairs are the trickiest of the three — not because the logic is harder, but because the pair is camouflaged. A hidden pair occurs when two candidates appear in exactly two cells within a unit, and those candidates do not appear anywhere else in that unit. Unlike naked pairs, the pair cells also contain other candidates, which hides the pair in plain sight.
The key insight: If two digits can only go in two specific cells within a unit, those two cells are locked for those two digits — regardless of what other candidates are also in those cells. Once you identify the hidden pair, remove all non-pair candidates from those two cells. The cells become a naked pair, and you can then eliminate from the rest of the unit.
Worked example: In a row, digits 6 and 9 appear as candidates in exactly two cells: Cell A has {2, 4, 6, 9} and Cell B has {1, 6, 7, 9}. Because 6 and 9 cannot go anywhere else in this row, they are locked to Cells A and B. Remove 2, 4 from Cell A and 1, 7 from Cell B. You are left with {6, 9} in both cells — a naked pair that then eliminates 6 and 9 from the rest of the row.
How to spot them: Shift your focus from cells to digits. For each digit in a unit, note which cells it can go into. When two different digits share the same two cells — and only those two — you have a hidden pair.
Using All Three Together
In practice, you apply these techniques in layers. Start with pointing pairs on each box (fast to scan, high yield). Then check for naked pairs in each unit. Finally, look for hidden pairs when naked pairs come up empty.
This is the standard intermediate solving order:
- Naked and hidden singles (basics)
- Pointing pairs / locked candidates
- Naked pairs (and triples)
- Hidden pairs (and triples)
- More advanced techniques if still stuck
Once you are comfortable with pairs, the natural next step is X-Wing and Swordfish for row/column patterns, and for an advanced pairs extension, explore the Sue de Coq technique — which builds directly on the locked candidates logic of pointing pairs.
Frequently Asked Questions
What is a naked pair in Sudoku?
A naked pair is two cells in the same unit that each contain exactly the same two candidates — and only those two. Because those two digits must occupy those two cells, you can safely remove them from every other cell in the same unit.
What is a hidden pair in Sudoku?
A hidden pair occurs when two candidates appear in exactly two cells within a unit, and those candidates don't appear anywhere else in that unit. Even though the pair cells contain other candidates too, those two digits are locked there — so you can remove all other candidates from the pair cells.
What are pointing pairs in Sudoku?
Pointing pairs (also called locked candidates) occur when a candidate digit appears in only one row or column within a 3×3 box. Because that digit must go in one of those cells, you can eliminate it from the rest of that row or column outside the box.
In what order should I learn these three pair techniques?
Learn pointing pairs first — they are the simplest and appear most frequently in medium puzzles. Then naked pairs, which require spotting two cells with identical candidates. Hidden pairs are the trickiest because the pair is camouflaged by extra candidates, so leave them for last.
What comes after naked and hidden pairs?
Once pairs feel natural, the next step is naked and hidden triples, then X-Wing, and eventually more advanced inference chains. Sue de Coq is an advanced variation that builds directly on pairs logic.