If you have moved beyond the basics of Sudoku and find yourself staring at a grid that refuses to yield its next number, you are ready to learn two of the most powerful intermediate techniques in the game: naked pairs and naked triples. These strategies belong to a family of solving methods called candidate elimination, and once you understand them, you will be able to crack puzzles that would otherwise leave you completely stuck. This guide explains both techniques from the ground up, walks you through concrete worked examples, and shows you exactly how to apply them in your own games.
Understanding Candidates: The Foundation You Need First
Before we can talk about naked pairs and naked triples, we need to make sure you are comfortable with the concept of candidates (sometimes called pencil marks). A candidate is simply any number that could legally go in a given cell based on the current state of the puzzle. If a cell is empty, its candidates are all the digits from 1 to 9 that do not already appear in that cell’s row, column, or 3×3 box.
Many Sudoku players — and most Sudoku apps, including the one here on playsudoku.org — allow you to write small numbers inside empty cells to track these possibilities. This practice is called pencil marking, and it is absolutely essential for techniques like naked pairs and naked triples. If you have been solving Sudoku by logic and intuition alone without writing candidates, these strategies are your invitation to level up.
Once you have filled in the candidates for every empty cell in a puzzle (or at least for a region you are examining), patterns begin to emerge. Naked pairs and naked triples are two of the most common and useful of these patterns.
What Is a Naked Pair?
A naked pair occurs when exactly two cells in the same row, column, or box each contain exactly the same two candidates — and no other candidates. Because those two cells are the only homes available for those two digits within that unit, the two digits must go in those two cells. We may not know which digit goes in which cell yet, but we know with absolute certainty that no other cell in the same row, column, or box can contain either of those two digits.
This is the elimination power of a naked pair: it allows you to remove those two candidate numbers from every other cell in the shared unit.
Worked Example: Spotting a Naked Pair in a Row
Let’s walk through a concrete example. Imagine you are looking at Row 5 of a Sudoku puzzle. After pencil marking, the empty cells in that row have the following candidates:
- Column 1: {3, 7}
- Column 2: {2, 5, 7}
- Column 4: {3, 7}
- Column 6: {1, 2, 5}
- Column 8: {2, 5, 9}
- Column 9: {1, 9}
Look carefully at the cells in Column 1 and Column 4. Both cells contain exactly {3, 7} — nothing more, nothing less. That is a naked pair. The digits 3 and 7 must occupy those two cells. It does not matter which order they go in, but they cannot appear anywhere else in Row 5.
What does this mean for the other cells in that row? You can now eliminate 3 and 7 from every other candidate list in Row 5. The cell in Column 2 currently has {2, 5, 7} — after elimination it becomes {2, 5}. The other cells that did not contain 3 or 7 are unaffected. This might seem like a small gain, but reducing a cell from three candidates to two is often exactly the step needed to unlock a chain of deductions that solves the puzzle.
Naked pairs can appear in a row, a column, or a 3×3 box. Always scan all three types of units when you are looking for them.
What Is a Naked Triple?
A naked triple extends the same logic to three cells and three digits. It occurs when three cells in the same unit collectively contain only three distinct candidates, distributed across those three cells in any combination. The key word is collectively — the individual cells do not each need to contain all three digits.
This is where many players get confused, so let’s be precise. A naked triple is valid if three cells in a unit contain candidates drawn exclusively from a set of three numbers, and no cell in the triple contains a candidate outside that set. The possible distributions look like this:
- All three cells have exactly the same three candidates: {4, 6, 8}, {4, 6, 8}, {4, 6, 8}
- Two cells have three candidates and one has two: {4, 6, 8}, {4, 6, 8}, {4, 6}
- Each cell has a different pair: {4, 6}, {6, 8}, {4, 8}
- Mixed: {4, 6, 8}, {4, 6}, {6, 8}
In every case, those three digits are confined to those three cells, and can be eliminated from every other cell in the same unit.
Worked Example: Finding a Naked Triple in a Box
Let’s look at a 3×3 box. After pencil marking, the empty cells in this box have the following candidates:
- Cell A: {2, 5}
- Cell B: {2, 9}
- Cell C: {5, 9}
- Cell D: {1, 2, 5, 9}
- Cell E: {1, 3}
Cells A, B, and C contain candidates drawn exclusively from the set {2, 5, 9}. Cell A has {2, 5}, Cell B has {2, 9}, and Cell C has {5, 9}. Together, they cover all three digits and no others. That is a naked triple.
The consequence is powerful: digits 2, 5, and 9 are locked inside Cells A, B, and C. They cannot appear in any other cell in this box. Cell D currently shows {1, 2, 5, 9} — after applying the naked triple elimination, it becomes simply {1}. That means Cell D is solved! You can place the number 1 in Cell D immediately, and that newly placed digit might then trigger further eliminations across its row and column.
This chain reaction is what makes naked triples so satisfying to find. A single discovery can cascade into solving several cells at once.
How to Search for Naked Pairs and Triples Efficiently
Knowing what you are looking for is one thing — finding naked pairs and triples efficiently in a real puzzle is another. Here is a practical process you can follow:
- Complete your pencil marks first. You cannot reliably find naked pairs or triples unless your candidate lists are accurate and up to date. Spend time at the start of each session making sure every empty cell has the correct candidates recorded.
- Scan for cells with only two candidates. These are your starting points. Any cell with just two candidates is a potential member of a naked pair or triple.
- Look for matching pairs within a unit. If you find a cell with {X, Y}, search the rest of its row, column, and box for another cell that also contains only {X, Y}. If you find one, you have a naked pair — eliminate X and Y from all other cells in that unit.
- Group two-candidate cells for triple hunting. Take any cell with two candidates and ask: is there another cell in the same unit whose candidates, combined with this cell’s, still total only three distinct digits? If yes, search for a third cell in the same unit whose candidates are also drawn from that same set of three. If you find it, you have a naked triple.
- Check boxes, rows, and columns separately. A naked pair or triple that exists in a box might not be aligned along a row or column, and vice versa. Examine each unit type independently.
- Update your candidates immediately. As soon as you apply an elimination, update all affected cells before moving on. Fresh pencil marks help you spot new opportunities.
With practice, your eye will begin to pick out these patterns quickly. Many experienced Sudoku players can spot a naked pair in seconds once they have trained themselves to look for cells with minimal candidates.
Naked Pairs and Triples vs. Hidden Pairs and Triples
It is worth briefly mentioning the related techniques of hidden pairs and hidden triples, because players often encounter both around the same time and can confuse them.
A naked pair is visible because the matching cells contain only those two digits as candidates. A hidden pair, by contrast, occurs when two digits appear as candidates in exactly two cells within a unit, but those cells also contain other candidates alongside them. The pair is “hidden” among extra noise. The elimination effect is different: with a hidden pair, you eliminate all the other candidates from those two cells, rather than eliminating the pair’s digits from the rest of the unit.
Similarly, a hidden triple involves three digits that appear only in three specific cells within a unit, even though those cells have additional candidates cluttering them. Finding hidden pairs and triples is generally harder than finding naked ones, because you have to scan by digit rather than by cell. As you build experience with naked pairs and naked triples, hidden pairs and triples become your natural next challenge.
There is also a technique called a naked quad — four cells in a unit sharing exactly four candidates between them — but this is significantly rarer and harder to spot, so most players focus on pairs and triples first.
Key Takeaways
- A naked pair is two cells in the same row, column, or box that each contain exactly the same two candidates. Those two digits can be eliminated from every other cell in that unit.
- A naked triple is three cells in the same unit whose candidates, taken together, include exactly three distinct digits. Those three digits can be eliminated from every other cell in that unit.
- The individual cells in a naked triple do not each need to contain all three digits — they just cannot contain any digit outside the trio.
- Both techniques rely on accurate pencil marks. Make sure your candidates are complete and up to date before searching.
- Eliminating candidates can trigger further deductions, sometimes solving multiple cells at once and cracking open a stalled puzzle.
- Naked pairs and triples are the foundation for understanding related techniques like hidden pairs, hidden triples, and pointing pairs.
Naked pairs and naked triples are genuinely exciting milestones in your Sudoku journey. The moment you spot your first naked triple and watch a formerly impossible puzzle start to unravel is one of the great rewards the game has to offer. Keep a pencil — or use the notes feature on playsudoku.org — and start hunting for those confined candidates today. The more puzzles you practice on, the faster these patterns will jump out at you, and the deeper and more rewarding your Sudoku experience will become.