Three digits confined to three cells within a unit. Clear everything else from those cells.
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.
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.
Let's find a Hidden Triple in row 1. After basic techniques, row 1 still has several empty cells with dense pencil marks.
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.
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.
Step 3: After elimination, the cells simplify to {5, 7}, {6, 7}, and {5, 6}. The puzzle becomes much more tractable.
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