Map each unplaced digit in a unit to the cells that can hold it. If three digits are confined to the same three cells, strip every other candidate from those cells. Nothing is placed directly, but the three cells collapse into a workable Naked Triple.
What Is It?
A Hidden Triple is the three-digit extension of a Hidden Pair. Three digits appear as candidates in exactly three cells within a unit, and those digits don't appear in any other cell of that unit. Since all three digits must go in those three cells, every other candidate in those cells can be removed.
Hidden Triples are genuinely difficult to spot manually. The three cells will usually have many other candidates cluttering the view, and you need to recognize that three specific digits are restricted to these three positions. Most solvers encounter Hidden Triples infrequently. They appear in Hard and Extreme puzzles.
Like Hidden Pairs, discovering a Hidden Triple doesn't directly place any digit. Instead, it dramatically simplifies the three cells, often revealing Naked Singles, Naked Pairs, or Locked Candidates.
How It Works
Focus on digits rather than cells. Within a unit, map each unplaced digit to the cells where it can go. If three digits share exactly the same three cells (and appear in no other cells), that's a Hidden Triple.
Suppose in column 2, digit 1 can go in R3C2, R5C2, and R9C2. Digit 6 can go in R3C2 and R9C2. Digit 8 can go in R3C2, R5C2, and R9C2. Check: digits 1, 6, and 8 are all confined to the cells R3C2, R5C2, and R9C2 (with 6 only needing two of the three). Since these three digits must occupy these three cells, remove all other candidates from those cells.
Note that not every digit needs to appear in all three cells. In the example above, digit 6 only appears in two of the three cells. That's perfectly valid. The key condition is that no digit appears outside the three cells.
After removing extra candidates, the three cells might become {1,6,8}, {1,8}, and {1,6,8}, effectively a Naked Triple that's much easier to work with.
Worked Example
Let's find a Hidden Triple in row 1. After basic techniques, row 1 still has several empty cells with dense pencil marks.
In row 1, digits {5, 6, 7} only appear in cells R1C1, R1C3, R1C4.
Step 1: Map digit positions in row 1. Digit 5 can go in R1C1 and R1C4. Digit 6 can go in R1C3 and R1C4. Digit 7 can go in R1C1 and R1C3. These three digits {5, 6, 7} are confined to exactly three cells: R1C1, R1C3, and R1C4.
{5, 6, 7} are hidden in R1C1, R1C3, R1C4. Remove other candidates from these cells.
Step 2: Since digits 5, 6, and 7 must fill R1C1, R1C3, and R1C4, any other candidates in those cells can be removed. R1C1 has {5, 7, 8}, remove 8. R1C3 has {4, 6, 7}, remove 4. R1C4 has {5, 6, 9}, remove 9.
Eliminated {4, 8, 9} from R1C1, R1C3, R1C4.
Step 3: After elimination, the cells simplify to {5, 7}, {6, 7}, and {5, 6}. The puzzle becomes much more tractable.
Frequently Asked Questions
Does each of the three digits have to appear in all three cells?
No. A digit may be restricted to only two of the three cells and the Hidden Triple still holds. The condition that matters is the other direction: none of the three digits may appear anywhere outside those three cells in the unit. If one does, the pattern fails.
How do I find a Hidden Triple?
Work from digits to cells, not cells to digits. Within one unit, write down the cells still available to each unplaced digit, then look for three digits whose lists sit inside the same three cells. Pencil marks are practically essential here; mental scanning alone is extremely difficult.
How is a Hidden Triple different from a Hidden Pair?
Only in size. A Hidden Pair is two digits confined to two cells; a Hidden Triple is three digits confined to three cells. The action is the same in both cases — clear all other candidates from the pattern’s cells — but the triple is much harder to see and turns up far less often.
Are Hidden Triples worth hunting for?
Not on an early pass. They are rare and appear mainly in Hard and Extreme puzzles, so reach for one only when you are stuck and have exhausted singles, Locked Candidates and pairs. When a Hidden Triple does turn up, clearing three cluttered cells frequently unblocks a substantial part of the grid.
What do I gain from a Hidden Triple if it does not place a digit?
You gain three much cleaner cells. Removing the clutter often leaves something like {1,6,8}, {1,8} and {1,6,8}, which is a Naked Triple you can work with directly. Naked Singles, Naked Pairs and Locked Candidates commonly surface immediately afterwards, so re-scan the unit and its intersections.
Key Points to Remember
- Map each digit to its possible cells within a unit. Look for three digits that share exactly three cells.
- Not every digit needs to appear in all three cells, but each digit must be confined to only those three cells.
- Hidden Triples are rare. Don't spend time hunting for them unless you're stuck and have exhausted pairs and Locked Candidates.
- Using pencil marks is practically essential for finding Hidden Triples. Mental scanning alone is extremely difficult.
- After cleaning the triple's cells, re-scan for simpler techniques. The elimination often unblocks the puzzle significantly.
The best way to master Hidden Triple is to practice spotting it in real puzzles.