Naked Triple
Description
Find three cells in the same row, column or 3x3 block whose complete candidate lists contain only three different digits between them. Those cells form a Naked Triple. Keep their notes, and remove those three digits from every other cell in that group.
Unlike a Naked Pair, the lists need not match. Each cell may have two or three candidates. For example, {1,2}, {1,3}, {2,3} form a triple: together they use only 1, 2 and 3. All three cells could also contain {1,2,3}. Count the different digits across the complete lists, not the number of notes in each cell.
Why? The three cells must contain three different digits, and their notes allow only those three. They must use each digit once, in some order. No other cell in their shared group can contain any of those digits, even before you know which digit goes in which cell.
A Naked Triple eliminates candidates. It may reveal a Naked Single or a Hidden Single, but several further eliminations may be needed before you can fill a cell. The examples below show both kinds of continuation.
We use pencil notes throughout. Green candidates stay and red candidates are removed. Yellow highlights show every other occurrence of the digits being discussed; the relevant group is shaded.
Example 1. A triple in a block reveals a single
Example 2. A triple leads to another elimination
The second example uses Claiming Candidates after the triple. In the demo, another triple creates a Naked Pair before a single appears. A triple is useful as soon as it removes candidates; the next step depends on the resulting notes.
Demo
How to find Naked Triples
- Use complete, up-to-date pencil notes. Look for singles and pairs first.
- In one row, column or block, look at cells with two or three candidates.
- Choose three cells and combine their entire candidate lists. There must be exactly three different digits altogether. Each cell may contain a different selection of those digits.
- Keep the triple's notes. Remove its three digits wherever they occur in other cells of the shared group.
- Recheck for singles. If none appear, continue looking for candidate eliminations using the updated notes. A placement may need several more deductions.
Highlighting all three digits helps you follow the pattern, but it does not replace checking each cell's complete list. If a cell has only one candidate, place that Naked Single first.
Count the digits across all three cells
{1,2}, {1,3}, {2,3} is a Naked Triple when the cells share a group. No cell contains all three digits, and no two cells form a Naked Pair. Their three combined lists are what reserve 1, 2 and 3.
{1,4}, {4,5,9}, {5,9} is not a Naked Triple: it contains four different digits. Having two or three notes in each cell is not enough. The demo's final check shows this on a real position. Likewise, an extra candidate outside your chosen three digits invalidates the triple.
All three cells must share one group. They need not be adjacent. Three cells scattered across the grid do not form a Naked Triple just because their candidate lists use the same three digits.
Where to remove candidates
Remove the triple's digits only from other cells in a group shared by all three cells. Keep every candidate inside the triple and all unrelated candidates outside it. A cell that sees just one or two members of the triple is not restricted by this rule alone.
If the three cells share both a block and a row or column, check each shared group separately. There need not be a copy of every digit to remove. Even one candidate removal can help; if there are no candidates to remove, recognizing the triple makes no immediate progress.
Triples, pairs and pointing triples
A Naked Pair reserves two digits for two cells. A Naked Triple reserves three digits for three cells. Both remove their digits from other cells in a shared group; a triple's three lists need not be identical.
A pointing triple concerns one digit with three possible positions in a block, all aligned in one row or column. It does not require three small candidate lists. See Pointing Candidates for that intersection rule.
Hidden subsets work in the opposite direction, as in the Hidden Pair lesson: they remove other digits from the subset's own cells. With six empty cells in a group, a Naked Triple has a complementary Hidden Triple in the other three cells. These are two ways to describe the same eliminations; the examples do not imply there is only one valid deduction.
Try it yourself
These prepared positions come from our puzzle library. Singles, intersections and both pair techniques have already been exhausted, and the links preserve the resulting notes. Find the triple and remove its candidates from the other cells in the group. Then inspect what changed.
- Sudoku #1 — find a triple in a column, then look for a single.
- Sudoku #2 — find a triple in a block, then look for a single.
- Sudoku #3 — find a triple in a row, then keep eliminating candidates.
Use Hint to check each deduction, apply it, then request the next hint. The first two exercises reveal a Hidden Single immediately. The third needs Pointing Candidates and Claiming Candidates before a single becomes available. These are selected continuations, not a fixed sequence for every triple.
Naked Triple hints are available in Expert and Extreme games, with pencil notes. All three practice links open directly in pencil mode.
See also
- Review Sudoku Rules for why the three cells must contain different digits.
- Start with Naked Pair for the same reasoning with two cells.
- Review Naked Single and Hidden Single to recognize possible placements after eliminations.
- Review Claiming Candidates to follow the second illustration's next deduction.
- Continue with Naked Quadruple to reserve four digits across four complete candidate lists.
- Play Expert Sudoku online to combine triples with singles, pairs and intersections.