SuuudokuuuNaked Triple Sudoku Technique
Updated
A naked triple is three cells in the same unit whose candidates, taken together, use only three different digits, which reserves those digits for the three cells and clears them from the rest of the unit.
When a naked triple applies
The trap with triples is expecting three identical candidate lists. That is only one of the possible shapes. A valid triple over the digits a, b and c can be made of any mix of {a,b,c}, {a,b}, {a,c} and {b,c} cells, as long as the union across the three cells is exactly three digits and no cell brings in a fourth.
Three cells that can only hold three digits will consume all three, one each. Since a unit contains every digit exactly once, those digits are no longer available to any other cell in the row, column or box that holds the triple.
Naked triples appear in units with five or six blanks. Fewer blanks and the puzzle usually collapses to singles first; more blanks and the candidate lists are still too wide for three cells to share only three digits.
Worked example
Column 2 has five empty cells. Three of them carry only 7, 8 and 9 between them: r1c2 shows 7 and 8, r4c2 shows 7, 8 and 9, and r9c2 shows 7, 8 and 9. Note the mismatch in size, which is exactly why triples are missed so often. The union is still just three digits.
Those three digits are therefore locked into those three cells. r3c2 held 1, 2, 7 and 8 and gives up the 7 and the 8. r8c2 held 1, 2, 8 and 9 and gives up the 8 and the 9. Both are left holding 1 and 2, which is a fresh naked pair and an immediate second deduction.
How to spot a naked triple
- Pick a unit with five or six blanksRows, columns and boxes in that range are where triples live. Write out the candidates before you start looking.
- Collect cells with two or three candidatesAny cell with four or more candidates cannot belong to a triple, so cross those out of consideration immediately.
- Test combinations for a three-digit unionTake three of the surviving cells and merge their candidate lists. If the merged list has exactly three digits, you have a triple.
- Erase those digits from the rest of the unitRemove all three digits from every other cell in the unit, then rescan for the naked or hidden single the removal usually exposes.
Common mistakes
- Insisting that all three cells show all three candidates. Subsets of the triple are perfectly valid as long as no fourth digit appears.
- Accepting a union of four digits. Three cells covering four digits proves nothing at all.
- Eliminating from the triple cells. They keep every candidate they had; the rest of the unit loses the three digits.
- Overlooking the box. If all three cells also share a box, the same three digits can be cleared from the box as well as from the line.
Naked triple FAQ
Do all three cells need identical candidates?
No. The shapes 3-3-3, 3-3-2, 3-2-2 and 2-2-2 all work. The only requirement is that the union of the three candidate lists contains exactly three digits.
Can a naked triple be made of three cells with two candidates each?
Yes, and this is the classic ring shape: 1-2, 2-3 and 1-3. The union is 1, 2 and 3, so the triple is valid even though no cell shows all three digits.
Is a naked triple the same as a hidden triple?
No. A naked triple is found by looking at cells and counting digits. A hidden triple is found by looking at digits and counting cells, and it removes candidates from the triple cells rather than from their neighbours.
Why do solvers rank the triple above the pair?
Because there are far more three-cell combinations to test than two-cell ones. The reasoning is identical, but the search cost is higher, so Suuudokuuu tries pairs first.