The Naked Quad is a powerful elimination strategy. It’s the big brother of the Naked Pair (two numbers) and Naked Triple (three numbers). While it looks intimidating because it involves four cells and four numbers, the logic is exactly the same.
What is a Naked Quad?
A Naked Quad occurs when four cells in the same unit (a row, column, or box) contain only the same four candidate numbers.
Because those four numbers must occupy those four specific cells (in some order), those four numbers cannot appear in any other cell in that same row, column, or box.
Interactive Example
Click "Apply Logic" to see the strategy in action.
Real Example Explanation
In the interactive example above, look at Column 4:
- Spot the Quad: The four cells highlighted in Green contain the candidates
{1, 3, 4, 5}. - Verify the Set: No other numbers (like 2, 6, 7, 8, 9) appear in these four cells.
- The Logic: Since we have four cells and exactly four numbers to fill them, these numbers are "locked" here.
- The Elimination: We can eliminate
1, 3, 4, 5from any other cell in this column. In this case, we remove a 1 from the cell highlighted in Red (R3C4).
How it Looks (The "Four-Way Puzzle")
The "naked" part means these numbers aren't hidden behind other candidates. However, the four numbers don't have to appear in every cell. It might look like this:
- Cell A:
{1, 2} - Cell B:
{2, 3} - Cell C:
{3, 4} - Cell D:
{1, 4}
In this set, we have four cells (A, B, C, D) and exactly four numbers (1, 2, 3, 4). No matter how you arrange them, those four numbers are "used up" by those four cells.
How to Execute the Strategy
- Spot the Group: Scan a row, column, or box for four cells that share a limited pool of candidates.
- Key Check: Count all the different candidate numbers in those four cells. If the total is exactly four, you’ve found a Naked Quad.
- The "Locked" Logic: Ask yourself: "If I put a 1 anywhere else in this row, would I have enough numbers left to fill those four cells?" The answer will always be no.
- The Elimination: Once you identify the Quad, look at every other cell in that unit. If any of those other cells have 1, 2, 3, or 4 written as a candidate, erase them.
Pro Tip: Look for the "Leftovers"
Naked Quads are rare and hard to spot because of the clutter.
Since a row has 9 cells, if 4 cells form a Naked Quad, the other 5 cells are also restricted. Sometimes it’s easier to look at the 5 cells that aren't part of the quad. If those 5 cells look "busy" or contain a specific set of numbers, check if the remaining 4 are naked!
Often, finding a Naked Quad leaves behind a much simpler Hidden Single or Hidden Pair in the rest of the unit.
Summary
- Logic: 4 cells, 4 numbers.
- Result: Remove those 4 numbers from the rest of the unit.
- Difficulty: Hard to spot, but easy to verify once found.