How to Master the Naked Quads Strategy in Sudoku
When Pairs and Triples aren’t enough to break a stubborn deadlock in Hard and Expert puzzles, you need to look for larger candidate combinations. The Naked Quad technique is the largest subset elimination strategy in Sudoku. Pretty similar to the “Naked Triple,” but based on four candidates instead of three, so it’s a bit harder to spot.
By identifying four interconnected cells that lock four specific digits, you can perform a massive cleanup of pencil notes across an entire row, column, or block.
The Logic Behind a Naked Quad
A Naked Quad occurs when four cells inside the same unit (row, column, or block) contain a total combination of no more than four unique candidate digits.
Look at this example:
The highlighted cells contain only values 2, 4, 6, and 8.
Because four cells are strictly restricted to four unique numbers, those four cells are legally locked. Even if we don’t know the exact order of the numbers yet, we know with 100% certainty that 2, 4, 6, and 8 will be absorbed by these four spots.
That means 2, 4, 6, and 8 can’t appear in other cells of the unit and can be deleted.
The Golden Rule of Quads (Variations)
Just like with Naked Triples, all four cells do not need to contain all four digits. A cell in a Naked Quad can contain two, three, or four of the candidates.
For example, a perfectly valid Naked Quad of (2, 4, 6 and 8) can look like this:
- Cell A: 2 & 4
- Cell B: 4, 6 & 8
- Cell C: 2 & 6
- Cell D: 6 & 8
As long as the total pool of candidates across all four cells equals exactly four unique digits (2, 4, 6, and 8), the Quad is valid and locked!
Step-by-Step Elimination
- Scan for a shared pool: Find four cells in a unit whose combined pencil notes only contain four unique numbers.
- Lock the candidates: Confirm that no fifth number is hiding inside any of those four cells.
- Clean the unit: Go to every other empty cell in that same row, column, or block, and delete 2, 4, 6, and 8 from their pencil notes.
Where to Find Quads: Rows, Columns, and Blocks
Naked Quads can appear anywhere on the grid, acting as a powerful broom to clear out clutter:
- In 3×3 Blocks: Clearing four candidates from the remaining empty cells of a box often immediately exposes a Naked Single or Naked Pair.
- In Lines: A Naked Quad can also be found in a column or a row. When you eliminate four numbers along a full horizontal or vertical line, it creates a massive domino effect across intersecting blocks.
Pro Tip: The Hidden/Naked Duality
In Sudoku math, a Naked Quad in a unit always has a hidden counterpart! If a unit has 9 cells and you find a Naked Quad (4 cells), the remaining 5 cells will contain the other 5 numbers. If 4 of those are filled, the remaining 5th cell is actually a Hidden Single or Hidden Pair! Training your eyes to spot Quads helps you see the entire grid in balance.
Ready to hunt for Quads? Put your expert scanning to the test on our Expert Sudoku Puzzles, turn on your pencil notes, and sweep the board clean!