Sudoku Strategies: Naked Quads
Naked Quads in Sudoku
A Naked Quad (or Naked Quadruple) in Sudoku is an advanced solving technique where a set of four cells within the same house (row, column, or 3x3 box) collectively contain only four distinct candidate numbers among them.
Detailed Explanation
The core principle of a Naked Quad is that these specific four digits must be the solutions for those specific four cells within that house. This is because there are exactly four available spots for exactly four numbers. The exact position of each number within the quad might not be immediately known, but it is certain that they cannot appear anywhere else in that same house.
The key rules and characteristics are:
- Same House: All four cells must belong to the same row, column, or 3x3 block.
- Four Cells, Four Candidates: When you combine all the candidates from the four cells, there should be a total of only four unique digits (e.g., {1, 2, 3, 5}).
- Candidate Distribution: Each of the four cells might contain two, three, or all four of these candidates, as long as no other candidates are present in any of the four cells. It is not necessary that every cell contains all four digits.
- The Elimination: Because these four numbers are "locked" into the four cells of the quad, you can eliminate all instances of these four numbers as candidates from all other cells in that same house.
Example
Consider a row "F" where four cells ("F2","F4","F5", and "F6") have the following candidates:
- Cell F2: {1, 3}
- Cell F4: {1, 2, 3}
- Cell F5: {3, 5}
- Cell F6: {1, 2, 5}
The combined candidates for these four cells are {1, 2, 3, 5}, which is a set of four unique digits. This forms a Naked Quad.
Action: You can now remove candidates 1, 2, 3, and 5 from all the other five cells in that same row. In this case, you can remove 3 from cell "F9".
How to Spot One
Naked Quads are relatively rare and can be difficult to spot manually. The best way to find them is to:
- Use pencil marks (writing all possible candidates in each empty cell) across the entire grid.
- Scan each row, column, and 3x3 box, looking for a set of exactly four cells that, taken together, contain only four unique candidate numbers.
- Ensure that no three of these cells form a smaller Naked Triple, which would be a more efficient elimination.
By systematically checking the candidate lists, you can identify and utilize this powerful advanced strategy.
