Hidden Triple

Interactive Tutorial

A Hidden Triple extends the Hidden Pair concept to three cells. When three digits can only appear in three cells within a unit, those cells must contain those digits. All other candidates can be eliminated from those three cells.

How It Works

The Mental Shift

Hidden triples require digit-focused thinking — the opposite of naked triples:

The Pattern

Look for three digits in a row, column, or box where:

• Each of the three digits appears as candidates in at most three cells
• All three digits share the same set of three cells
• Neither digit appears anywhere else in that unit

Not All Cells Need All Digits!

Important: Just like hidden pairs, not every cell needs to contain all three digits. This is common and expected:

• One cell might have all three: {2, 5, 6}
• Another might have just two: {2, 6}
• A third might also have just two: {2, 5}

The key is that digits 2, 5, and 6 can only appear in these three cells — nowhere else in the unit.

The Logic

If digits {2, 5, 6} can only appear in R1C4, R1C7, and R1C9 within Row 1, then:

• These three cells must hold 2, 5, and 6
• Any other candidates in these cells can be eliminated

The triple is "hidden" because the cells typically contain many additional candidates that obscure the pattern.

How to Spot Hidden Triples

Step-by-Step Scanning

1. Pick a unit — Choose a row, column, or box to scan
2. For each digit, ask: "Where can this digit go?"
3. Count positions — Note digits that can only go in 2-3 cells
4. Find matching sets — Three digits confined to the same three cells = Hidden Triple

Using Focus Mode

Focus Mode makes hidden triples much easier to spot:

1. Tap a digit to highlight all cells containing it
2. Look for digits that appear in only 2-3 cells within a unit
3. Check if multiple digits share the same cells

Example

Look at Row 1 and ask: where can each digit go?

Row 1 Analysis:

• Digit 2: only in R1C4, R1C7, and R1C9
• Digit 5: only in R1C4 and R1C9
• Digit 6: only in R1C4 and R1C7
• Other digits: appear in more cells throughout the row

Digits {2, 5, 6} are all confined to the same three cells — this is a Hidden Triple!

Notice how not every cell contains all three digits:

• R1C4 has {2, 4, 5, 6, 7, 8} — contains 2, 5, 6
• R1C7 has {2, 4, 6, 9} — contains 2, 6 (missing 5!)
• R1C9 has {2, 4, 5, 7, 8, 9} — contains 2, 5 (missing 6!)

Since R1C4, R1C7, and R1C9 must contain 2, 5, and 6, we eliminate all other candidates:

Eliminations:

• R1C4: remove {4, 7, 8} → leaves {2, 5, 6}
• R1C7: remove {4, 9} → leaves {2, 6}
• R1C9: remove {4, 7, 8, 9} → leaves {2, 5}

puzzle: S9BD6BE2I7G62018S03DO0203017E096A1M5E6ID6060564620301B8D8060708090204030Z0Z017W035U055U7WB8068A8C0S01030607BOBW4A4D0903064405070L2Q10062S0109080403034T2K6K626C8K8L7P
mode: guided
technique: Hidden Triple
initial:
  layers:
    hints: true
steps:
  - text: >
      Where can digit 2 go in Row 1? Use Focus Mode to highlight all 2s.
    hint: subtle
    technique: HT
    state:
      focus:
        enabled: true
        digits: [2]

  - text: >
      Digit 2 only appears in R1C4, R1C7, and R1C9. Now check digits 5 and 6.
    hint: subtle
    technique: HT
    state:
      selection:
        cells: [R1C4, R1C7, R1C9]
      focus:
        enabled: true
        digits: [2]

  - text: >
      Digit 5 is only in R1C4 and R1C9. Digit 6 is only in R1C4 and R1C7. All three digits are confined to the same three cells!
    hint: obvious
    technique: HT
    state:
      selection:
        cells: [R1C4, R1C7, R1C9]
      focus:
        enabled: true
        digits: [2, 5, 6]

  - text: >
      These cells must contain {2,5,6}. Remove all other candidates: R1C4~4,7,8, R1C7~4,9, R1C9~4,7,8,9.
    hint: detailed
    technique: HT
    state:
      selection:
        cells: [R1C4, R1C7, R1C9]
      focus:
        enabled: true
        digits: [2, 5, 6]
settings:
  showCandidates: true
  showControls: true
  showDescription: true
  navigation: numbered

Hidden vs Naked

Both techniques achieve the same result — they lock three digits to three cells. The difference is perspective:

Pro tip: After finding a Hidden Triple and eliminating, the cells often form a Naked Triple or chain of Naked Pairs!

Tips

1. Use Focus Mode — Highlight one digit at a time to see where it can go
2. Count systematically — For each digit, count its possible positions in the unit
3. Look for "orphan" digits — Digits appearing in only 2-3 cells are your targets
4. Check all units — Hidden triples can appear in rows, columns, or boxes
5. Expect clutter — Unlike naked triples, the cells will have many extra candidates

Common Mistakes

• Expecting all digits in all cells — Not all three cells need all three digits
• Forgetting to eliminate — Remove ALL other candidates from the triple cells
• Wrong unit — Ensure all three digits are exclusive within the SAME row, column, or box

The Subset Principle

Both hidden and naked techniques follow the same fundamental rule:

• N cells with N candidates = those candidates locked to those cells
• Hidden view: N candidates in only N cells → eliminate extras from those cells
• Naked view: N cells with only N candidates → eliminate from other cells in unit

This scales to pairs (2), triples (3), and quads (4).

More Puzzles

• Hidden Triple ex. 1
• Hidden Triple ex. 2
• Hidden Triple ex. 3
• Hidden Triple ex. 4
• Hidden Triple ex. 5
• Hidden Triple ex. 6
• Hidden Triple ex. 7
• Hidden Triple ex. 8
• Hidden Triple ex. 9

Related Techniques

• Hidden Pair — Two digits in two cells
• Naked Triple — Same result, cell-focused perspective
• Naked Quad — Four cells with four candidates