Naked Quad in Sudoku
A Naked Quad extends the logic of Naked Pairs and Naked Triples. It locks four candidates into four cells in one row, column or box, so those digits can be removed from every other cell in that unit.
What is a Naked Quad?
Choose four unsolved cells in the same unit. If the union of their candidates contains exactly four different digits, those digits must occupy the four cells in some order. Each cell does not need to contain all four digits.
Once the pattern is confirmed, remove the four digits from the other cells in the unit. Do not remove them from the four cells that form the Naked Quad.
Example: a Naked Quad in row 4
- R4C1: {1,4}
- R4C3: {1,4,7}
- R4C6: {4,7,9}
- R4C8: {1,9}
Together these cells contain only 1, 4, 7 and 9. Those four digits are locked into the four cells, so matching candidates in the other cells of row 4 can be eliminated.
The yellow cells form the quad; red crosses mark candidates that can be removed.
How to find a Naked Quad
- Select one row, column or box.
- Start with cells that have few candidates.
- Combine the candidates of four cells.
- Check that the union contains exactly four digits.
- Remove those digits from the other cells in the unit.
If this feels difficult, review the Naked Triple first, then compare the elimination direction with a Hidden Quad.
Common mistakes
Requiring identical candidate lists
The four cells do not need identical notes. Only their combined set must contain exactly four digits.
Accepting five different candidates
A union of five or more digits is not a standard Naked Quad.
Removing candidates from the quad itself
The eliminations occur in the other cells of the same unit.
Summary
Four cells plus exactly four combined candidates lock those digits into the four cells. Remove the same candidates from the rest of the row, column or box.
Frequently asked questions
What is a Naked Quad in Sudoku?
A Naked Quad is formed when four cells in one row, column or box contain exactly four different candidates between them.
Must every cell contain all four candidates?
No. The union of the candidates in the four cells must contain exactly four digits, but each cell may contain only two or three of them.
Where are candidates removed after finding a Naked Quad?
Remove the four digits from the other cells in the same unit, not from the four cells that form the Naked Quad.
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