Hidden Quad in Sudoku
A Hidden Quad extends the logic of Hidden Pairs and Hidden Triples. Instead of counting the candidates inside cells, it tracks where four selected digits can appear within one row, column or box.
What is a Hidden Quad?
If four digits can appear only in four particular cells of one unit, those cells must eventually contain the four digits. The cells may currently contain extra candidates.
After confirming the Hidden Quad, remove every candidate from those four cells that is not one of the four target digits. This is the opposite elimination direction from a Naked Quad.
Example: a Hidden Quad in column 6
Digits 1, 2, 4 and 6 occur only in R1C6, R3C6, R6C6 and R8C6. They must occupy those four positions, so the unrelated candidates 5, 7, 8 and 9 shown in the cells can be removed.
The yellow cells are the only positions for 1, 2, 4 and 6; red crosses mark the extra candidates.
How to find a Hidden Quad
- Select one row, column or box.
- Map the possible positions of each unsolved digit.
- Choose four digits with relatively few positions.
- Check whether all their positions are confined to the same four cells.
- Remove unrelated candidates from those four cells.
Reviewing the Hidden Triple can make the position-based logic easier to see. Compare it with the Naked Quad to remember where eliminations occur.
Common mistakes
Expecting only four notes in the cells
Extra candidates are allowed and are exactly what the technique removes.
Requiring every digit in all four cells
A target digit may appear in only two or three of the cells, as long as all four digits are confined to the four-cell set.
Removing the target digits elsewhere
A Hidden Quad removes unrelated candidates inside the target cells.
Summary
When four digits in one unit can appear only in four cells, remove all other candidates from those four cells.
Frequently asked questions
What is a Hidden Quad in Sudoku?
A Hidden Quad is formed when four digits can appear only in four particular cells of one row, column or box.
Can Hidden Quad cells contain extra candidates?
Yes. Those extra candidates are removed after the Hidden Quad is confirmed.
How is a Hidden Quad different from a Naked Quad?
A Hidden Quad removes unrelated candidates from the four target cells; a Naked Quad removes its four digits from the other cells in the unit.
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