Hidden Quads in Sudoku: The Complete Guide

What is a Hidden Quad?

A hidden quad (also called a "hidden quadruple") occurs when four candidates appear in only four cells within a unit (row, column, or box), but those cells also contain many other candidates that "hide" the quad. Once you identify the four numbers that form the quad, you can eliminate all other candidates from those four cells.

Hidden quads are one of the rarest techniques in Sudoku—even experienced solvers may go months without encountering one.

Example:

In Row 3, candidates 1, 2, 5, and 8 appear in only four specific cells:

Cell A: {1, 2, 3, 4, 5, 6, 8}
Cell B: {1, 2, 3, 5, 6, 7, 8}
Cell C: {1, 2, 4, 5, 7, 8, 9}
Cell D: {1, 2, 5, 6, 8, 9}

No other cells in Row 3 contain 1, 2, 5, or 8. This means these four numbers must occupy these four cells. Eliminate 3, 4, 6 from Cell A; eliminate 3, 6, 7 from Cell B; eliminate 4, 7, 9 from Cell C; eliminate 6, 9 from Cell D, leaving {1, 2, 5, 8} in each cell.

Why Hidden Quads Matter

They're one of the rarest manual techniques—finding one is a badge of honor.
They simplify extremely crowded cells that seem impossibly complex.
They demonstrate complete mastery of subset logic.
They occasionally appear in expert-level puzzles where nothing else works.
They complete the hidden subset family (singles, pairs, triples, quads).

How to Spot a Hidden Quad

Focus on one unit at a time.
Pick a row, column, or box to analyze—preferably one with many complex cells.
Track where each candidate appears.
For each number 1-9, note which cells in that unit contain it as a candidate.
Look for four numbers in exactly four cells.
Find four candidates that appear in the same four cells and nowhere else in that unit.
Verify the cells have extra candidates.
If the four cells already contain only those four candidates, it's a naked quad, not hidden.
Eliminate other candidates from those cells.
Remove all candidates except the quad from those four cells.

Hidden Quad vs Other Hidden Subsets

The hidden subset family all works the same way:

Hidden pair: 2 candidates in only 2 cells → eliminate from those 2 cells
Hidden triple: 3 candidates in only 3 cells → eliminate from those 3 cells
Hidden quad: 4 candidates in only 4 cells → eliminate from those 4 cells

All eliminate inward within the subset cells. Hidden quads are simply the largest practical subset humans typically search for.

Step-by-Step Example

Let's examine Box 6 (middle-right box):

Box 6 cells (rows 4-6, columns 7-9):

Row 4, Col 7: {2, 3, 4, 6, 7, 9}
Row 4, Col 8: {1, 2, 3, 4, 5, 6, 7}
Row 4, Col 9: {2, 3, 4, 5, 6, 7, 9}
Row 5, Col 7: [filled with 8]
Row 5, Col 8: {1, 2, 3, 4, 5, 6}
Row 5, Col 9: [filled with 7]
Row 6, Col 7: {2, 3, 4, 6, 9}
Row 6, Col 8: {1, 2, 3, 4, 5, 6}
Row 6, Col 9: {2, 3, 4, 5, 6, 9}

Analysis: Let's track where each candidate appears:

1 appears in: Row 4-Col 8, Row 5-Col 8, Row 6-Col 8 (3 cells)
2 appears in: Row 4-Col 7, Row 4-Col 8, Row 4-Col 9, Row 5-Col 8, Row 6-Col 7, Row 6-Col 8, Row 6-Col 9 (7 cells)
3 appears in: All non-filled cells (7 cells)

This box doesn't have a hidden quad. Let me provide a theoretical clearer example:

Theoretical Example - Column 5:

Imagine Column 5 where candidates 2, 4, 7, and 9 appear in only four cells (rows 2, 3, 5, and 7), but those cells also contain many other candidates like 1, 3, 6, and 8.

Before:

Row 2: {1, 2, 3, 4, 6, 7, 9}
Row 3: {1, 2, 3, 4, 6, 7, 8, 9}
Row 5: {2, 3, 4, 6, 7, 8, 9}
Row 7: {1, 2, 4, 6, 7, 8, 9}

Hidden quad identified: {2, 4, 7, 9} are confined to these four cells (no other cells in Column 5 contain these numbers).

After elimination:

Row 2: {2, 4, 7, 9} (removed 1, 3, 6)
Row 3: {2, 4, 7, 9} (removed 1, 3, 6, 8)
Row 5: {2, 4, 7, 9} (removed 3, 6, 8)
Row 7: {2, 4, 7, 9} (removed 1, 6, 8)

Result: The hidden quad is now "exposed" and the cells are dramatically simplified.

Visual Example: Why They're Hidden

Scenario: In a box, you see four cells with 6-7 candidates each. They look impossibly complex.
Hidden pattern: Buried within all those candidates, four specific numbers (say 1, 3, 6, 9) appear nowhere else in the box.
Recognition: By systematically tracking where each number appears, you discover the hidden quad.
Transformation: After elimination, those four messy cells become clean {1, 3, 6, 9} sets.
Impact: This often triggers a cascade of naked singles and other patterns.

Strategies for Spotting Hidden Quads Quickly

Don't actively hunt for them
Hidden quads are so rare that spending time searching is usually counterproductive. They're more of a "last resort" technique.
Use systematic candidate tracking
If you do search, create a chart showing where each number 1-9 appears in a unit. The pattern may reveal itself.
Focus on crowded units
Units where most cells have 5+ candidates are the only places quads hide effectively.
Look for restricted candidates first
Numbers that appear in only 4-5 cells are more likely to be part of a hidden quad.
Consider other techniques first
Before searching for hidden quads, make absolutely sure you've exhausted all simpler options including X-Wing and XY-Wing.

Common Pitfalls

Missing the fifth cell: Make absolutely certain the four candidates appear in ONLY four cells, not five or more.
Confusing with naked quads: Hidden quads require elimination within the quad cells, not from other cells.
Incomplete elimination: Remove ALL other candidates from the four cells, not just some of them.
Wasting time searching: Hidden quads are so rare that you're usually better off trying other advanced techniques first.
Missing simpler patterns: Often what seems like a hidden quad situation actually contains simpler patterns you missed.

The Reality of Hidden Quads

Here's the truth about hidden quads:

Extremely rare: Many expert solvers have never encountered one in actual play.
Hard to spot: With so many candidates hiding the pattern, they're very difficult to recognize without systematic tracking.
Often avoidable: Many puzzles with potential hidden quads can be solved using other advanced techniques.
Satisfying when found: Despite (or because of) their rarity, finding one is immensely satisfying.
Theoretical importance: They complete your understanding of subset logic, even if you rarely use them.

Why Hidden Quads Set the Stage

Hidden quads represent the ultimate in subset elimination logic:

They complete your understanding of hidden subsets (singles → pairs → triples → quads)
They demonstrate that even the most complex cells can be simplified systematically
They prove you've mastered candidate tracking and pattern recognition
They prepare you for other advanced techniques that require meticulous analysis
They show that Sudoku has elegant patterns even in apparent chaos

Quick Recap

Technique	Pattern	Elimination	Rarity	Difficulty
Hidden Pair	2 in 2 cells	Inward	Occasional	Intermediate
Hidden Triple	3 in 3 cells	Inward	Rare	Intermediate
Hidden Quad	4 in 4 cells	Inward	Extremely Rare	Advanced
Naked Quad	4 cells, 4 candidates	Outward	Rare	Advanced

Final Thought

Hidden quads are Sudoku's "white whale"—elusive and legendary. Most solvers will never find one, but knowing they exist completes your theoretical toolkit. Are four numbers confined to just four very crowded cells? You might have found the rarest technique in Sudoku!

Frequently Asked Questions

What is a Hidden Quad in Sudoku?

A hidden quad occurs when four candidates appear in only four cells within a unit (row, column, or box), but those cells also contain many other candidates that hide the quad. Once identified, you can eliminate all other candidates from those four cells, leaving only the hidden quad. This is one of the rarest techniques in Sudoku.

How do I spot a Hidden Quad?

To spot hidden quads: 1) Focus on one unit at a time, 2) For each candidate number, note which cells contain it, 3) Look for four numbers that appear in exactly the same four cells (and nowhere else in that unit), 4) Eliminate all other candidates from those four cells, leaving only the quad.

What's the difference between Hidden Quads and Naked Quads?

Naked quads have four cells with only four candidates visible between them, and you eliminate outward from those cells. Hidden quads have four candidates that appear in only four cells (which have many extra candidates), and you eliminate inward within those cells. Naked quads eliminate from other cells; hidden quads clean up the quad cells themselves.

Why are Hidden Quads important?

Hidden quads are important because they're one of the rarest manual techniques, they simplify extremely crowded cells, they demonstrate complete mastery of subset logic, and they occasionally appear in expert-level puzzles where nothing else works.

When should I look for Hidden Quads?

Look for hidden quads only after exhausting all simpler techniques. They're extremely rare—many experienced solvers never encounter one. Focus on units with many cells containing 5-7 candidates each. Systematically track which four numbers appear in exactly four cells.

Ready to advance? Check out our complete strategy guide for more techniques.

Related Strategies

Once you've mastered hidden quads, these techniques build naturally:

Hidden Triples - The foundation for understanding quads
Hidden Pairs - The simpler hidden subset technique
Naked Quads - The complementary technique
X-Wing - Often more practical for advanced puzzles
XY-Wing - Advanced three-cell pattern

Practice Hidden Quads

Next up: Try XYZ-Wing for a more practical advanced technique (coming soon).

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