Quick Summary

When four cells in a house have candidates drawn strictly from four digits {A, B, C, D}, those four digits are locked into those four cells, eliminating them from the rest of the house.

Understanding the Naked Quad Technique

Naked Quads represent the largest practical naked subset used in standard 9×9 Sudoku. Finding four cells whose candidate union contains exactly four digits requires keen observation. Interestingly, every Naked Quad in a house is mathematically complementary to a Hidden Pair in that same house, meaning if you find the quad, you could also have found the pair.

Visual Examples

Green cells highlight the Naked Quad pattern, amber cells denote where candidates are affected, and struck-through pencil marks show the eliminations. Use the buttons or arrow keys to browse examples.

Example 1 of 5
Between them, R4C8, R5C8, R6C8, R9C8 in column 8 hold only 1,3,5,9. Those digits are locked to those 4 cells, so they can be removed from the rest of column 8.
Removes: 1 from R1C8, R8C8 · 3 from R1C8, R7C8 · 5 from R7C8 · 9 from R8C8

How to Spot & Solve a Naked Quad (Step-by-Step Guide)

The complete visual scanning and logical deduction process to execute this technique:

  • 1Look for four cells in the same unit whose pencil marks only contain four specific digits (e.g. 1, 4, 6, 9).
  • 2Verify that none of the four cells contain any candidate outside that four-digit set.
  • 3Because four slots must accommodate those four numbers, those digits are fully occupied by the group.
  • 4Erase those four candidate digits from every other cell in that row, column, or box.

Common Traps & Mistakes to Avoid

  • Missing cells with only 2 candidates that form part of the quad.
  • Spending too much time searching for a quad when looking for its complementary Hidden Pair or Hidden Single would be much faster.
  • Eliminating candidates from the quad cells themselves instead of from the remaining cells in the house.

Frequently Asked Questions

Why are Naked Quads so rare in puzzles?

Because most puzzles that have a Naked Quad can be solved faster by finding the complementary Hidden Pair or Hidden Triple in the remaining cells of that house.

Can a Naked Quad consist entirely of pairs?

Yes! For example, {1, 2}, {2, 3}, {3, 4}, and {1, 4} form a valid Naked Quad on digits {1, 2, 3, 4}.

Expand your repertoire by learning prerequisites and advanced counterparts:

Ready to Practice Naked Quad?

Try a puzzle in the Hard tier (Peak Score 5160), or browse all 25 techniques.