Hidden Quad

A Hidden Quad is the four-cell extension of Hidden Pair and Hidden Triple. When four digits can only appear in four cells within a unit, those cells must contain those digits. All other candidates can be eliminated from those four cells.

How It Works

The Mental Shift

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

The Pattern

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

• All four digits appear as candidates in at most four cells
• All four digits share the same four cells
• None of these digits appear anywhere else in that unit

Not All Cells Need All Digits!

Just like hidden pairs and triples, not every cell needs to contain all four digits:

• One cell might have all four: {3, 4, 5, 7}
• Another might have just two: {4, 7}
• Another might have three: {3, 4, 7}

The key is that digits 3, 4, 5, and 7 can only appear in these four cells.

The Logic

If only R5C7, R6C7, R7C7, and R8C7 can contain {3, 4, 5, 7} in Column 7, then:

• These four cells must hold 3, 4, 5, and 7
• Any other candidates in these cells can be eliminated

The quad is "hidden" because the cells may contain many other candidates that obscure the pattern.

How to Spot Hidden Quads

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 3-4 cells
4. Find matching sets — Four digits confined to the same four cells = Hidden Quad

When to Look

Hidden Quads are rare in practice:

1. Having four digits confined to exactly four cells is uncommon
2. Smaller techniques (pairs, triples) often solve the situation first
3. Finding the pattern requires checking many digit combinations

Most puzzles never require a Hidden Quad — if you encounter one, you're working on a difficult puzzle.

Example

Look at Column 7 and ask: where can each digit go?

Column 7 Analysis:

• Digit 3: only in R5C7
• Digit 4: only in R5C7, R6C7, R7C7, R8C7
• Digit 5: only in R7C7
• Digit 7: only in R5C7, R7C7, R8C7
• Other digits: appear in more cells or different positions

Digits {3, 4, 5, 7} are all confined to the same four cells — this is a Hidden Quad!

Notice the varying coverage:

• R5C7 has {2, 3, 4, 7, 9} — contains 3, 4, 7
• R6C7 has {4, 6} — contains only 4
• R7C7 has {4, 5, 6, 7} — contains 4, 5, 7
• R8C7 has {4, 7} — contains 4, 7

Since these four cells must contain 3, 4, 5, and 7, we eliminate all other candidates:

Eliminations:

• R5C7: remove {2, 9} → leaves {3, 4, 7}
• R6C7: no change needed (only has 4 and 6; 4 is kept)
• R7C7: remove {6} → leaves {4, 5, 7}
• R8C7: no change needed (only has 4 and 7)

puzzle: S9B06057R0N08077N02045W446106040943052ECY04D30N0205C32EAE05077O0403087O0601BGC4CC0536019S2M9K03011M0936022I08052K1G3W08091M40013CD6C2EI0201033U2I3601031O07051M1G0908
mode: guided
technique: Hidden Quad
initial:
  layers:
    hints: true
steps:
  - text: >
      Where can digit 3 go in Column 7? Use Focus Mode to highlight all 3s.
    hint: subtle
    technique: HQ
    state:
      focus:
        enabled: true
        digits: [3]

  - text: >
      Digit 3 only appears in R5C7. Now check digits 4, 5, and 7.
    hint: subtle
    technique: HQ
    state:
      selection:
        cells: [R5C7]
      focus:
        enabled: true
        digits: [3]

  - text: >
      Digit 4 is in R5C7, R6C7, R7C7, R8C7. Digit 5 is only in R7C7. Digit 7 is in R5C7, R7C7, R8C7. All four digits are confined to the same four cells!
    hint: obvious
    technique: HQ
    state:
      selection:
        cells: [R5C7, R6C7, R7C7, R8C7]
      focus:
        enabled: true
        digits: [3, 4, 5, 7]

  - text: >
      These cells must contain {3,4,5,7}. Remove other candidates: R5C7~2,9, R7C7~6.
    hint: detailed
    technique: HQ
    state:
      selection:
        cells: [R5C7, R6C7, R7C7, R8C7]
      focus:
        enabled: true
        digits: [3, 4, 5, 7]
settings:
  showCandidates: true
  showControls: true
  showDescription: true
  navigation: numbered

Hidden vs Naked

Both techniques lock four digits to four cells. The difference is perspective:

Tips

1. Try smaller sets first — Hidden pairs and triples are more common
2. Use Focus Mode — Highlight one digit at a time to see where it can go
3. Count systematically — For each digit, count its possible positions
4. Look for restricted digits — Digits appearing in only 3-4 cells are your targets
5. Trust the hint system — Hidden quads are difficult to spot manually

The Hidden Family

More Puzzles

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

Related Techniques

• Naked Quad — Same result, cell-focused perspective
• Hidden Triple — Three digits in three cells
• Hidden Pair — Two digits in two cells