Sudoku technique
Hidden Triple
Within a zone, three digits can only occupy three cells. Every other candidate in those three cells gets eliminated. The hard part is the sheer number of combinations to check — there are a lot more than with a pair.
A puzzle that requires it
Level Expert — the puzzle is shown twice: right below, and again in the demo that follows.
| 9 | 5 | |||||||
| 4 | 8 | 9 | 6 | |||||
| 7 | 5 | 3 | ||||||
| 8 | 1 | 4 | ||||||
| 7 | 1 | |||||||
| 3 | 6 | 9 | ||||||
| 9 | 4 | 3 | ||||||
| 5 | 2 | 1 | 7 | |||||
| 1 | 9 |
Demonstration
State of the grid right when the technique applies, after 12 earlier deductions.
Demo — watch first, you'll play right after.
- Technique's pattern
- Candidates removed
- Solved earlier
- Given (clue)
| 9 | 5 | |||||||
| 5 | 4 | 8 | 9 | 1 | 6 | |||
| 7 | 4 | 5 | 9 | 3 | ||||
| 8 | 9 | 1 | 4 | 3 | ||||
| 7 | 9 | 1 | ||||||
| 3 | 6 | 9 | ||||||
| 9 | 4 | 3 | 1 | |||||
| 5 | 3 | 9 | 2 | 1 | 7 | |||
| 7 | 4 | 1 | 9 |
Triplet caché
Dans cette zone, les chiffres 3, 4, 6 ne peuvent occuper que ces 3 cases. Ils les monopolisent : tout autre candidat y est éliminé.
Candidates removed:
- the 2 from cell L5C1
- the 2, 5 from cell L5C3
- the 2, 8 from cell L5C7
The Hidden Triple is the mirror of the Naked Triple: you no longer look for cells, you look for digits. When, in a zone, three digits can only go in the same three cells, those cells belong to them, even if they carry other candidates. Those other candidates disappear: the Hidden Triple cleans its own cells.
The principle
A zone is a row, a column or a box. Suppose that, in a zone, three digits, say 3, 6 and 9, have no possible place except the same three cells. The 3, the 6 and the 9 must go somewhere in the zone: they will go in those three cells, one each.
Those three cells are therefore fully taken by those three digits, whatever their other candidates. Remove those other candidates from their notes. The triple is “hidden” because its cells still look open to other digits, when they no longer are.
As with the Naked Triple, each digit does not need to appear in all three cells: the 3 may be possible in only two of them, and so on. What counts is that, between them, the three digits have no other place.
How to spot it
You need candidate notes. In a zone, take the digits one by one and note the cells where each remains possible. Look for three digits whose places, combined, cover only three cells, then erase every other candidate from those cells. This is the longest part of the technique: there are far more combinations to check than with a pair.
There is a detour. In a zone with n empty cells, a hidden group of k digits always matches a naked group of n − k cells: the other cells, forced to take the other digits, form that naked group. With six empty cells, a Hidden Triple therefore has a Naked Triple on the other three cells as its mirror: one of them is often quicker to see.
A worked example
In one column, the 3 is possible only in cells A and B, the 6 only in B and C, the 9 only in A and C. None of these digits appears elsewhere in the column. Together, the three therefore have only cells A, B and C.
Cell A has candidates 1, 3, 4 and 9, B has 2, 3 and 6, C has 5, 6, 7 and 9. Erase the 1 and the 4 from A, the 2 from B, the 5 and the 7 from C. That leaves 3 and 9 in A, 3 and 6 in B, 6 and 9 in C: a Naked Triple has appeared, and its three cells now hold only those digits.
Common mistakes
Confusion number one is with the Naked Triple. The Naked Triple eliminates its digits outside its cells. The Hidden Triple does the opposite: it eliminates the other candidates of its cells, and does not touch the neighbors.
Another mistake is to pick three digits when one of them is still possible in a fourth cell. The three digits must be confined to the same three cells. If just one of those digits is still possible elsewhere in the zone, there is no Hidden Triple.
When to use it
The Hidden Triple is expected at the Expert level, along with the Naked Triple, the quads and the X-Wing. It is one of the slowest techniques to spot, because the three digits are buried among other candidates.
- Expert sudoku
- Technique: the Naked Triple
- Technique: the Hidden Pair
- How to solve a sudoku
- Learn the techniques
Frequently asked questions
What is the difference between a Hidden Triple and a Naked Triple?
The Hidden Triple is recognized by its digits: three digits fit in only three cells of a zone, and the other candidates in those cells disappear. The Naked Triple is recognized by its cells: three cells have only three candidates between them, and those digits disappear from the other cells of the zone.
Must each digit of a Hidden Triple appear in all three cells?
No. Each can appear in only two of the three cells. It only matters that the three digits have, together, no other place in the zone than those three cells.
How are the Naked Triple and the Hidden Triple related?
In a zone with six empty cells, a Naked Triple on three cells implies a Hidden Triple on the other three, and the other way around. Both lead to the same eliminations: you pick whichever is easier to see.
Does a Hidden Triple place a digit?
No, it removes candidates from its own cells. Those eliminations can then leave a Naked or Hidden Single, which lets you place a digit.
Practice
Every technique helps remove candidates ; once a cell has only one left, you place it.
Three puzzles where Hidden Triple is the key move, served right before the step, with a coach.
Puzzle 1
Expert
The technique is used once in this puzzle
Puzzle 2
Expert
The technique is used once in this puzzle
Puzzle 3
Expert
The technique is used twice in this puzzle
Puzzles change every day.