Hidden Quad Sudoku Technique

Updated 11 August 2026

A hidden quad is four digits that between them can only go in the same four cells of a row, column or box, which reserves those cells for the four digits and removes every other candidate from them.

When a hidden quad applies

Hidden quads are the largest subset most solvers bother with, and they are also the rarest thing on this list that is still worth naming. Take four digits a unit still needs, collect every cell where any of them can land, and check whether that collection is exactly four cells. If it is, those four cells will take the four digits between them.

There is an important structural catch. In a unit with n empty cells, a hidden quad on four of them is the exact complement of a naked subset on the other n − 4 cells. When the unit has six, seven or eight blanks, that complement is a naked pair, triple or quad, and any solver checking naked subsets first will find the simpler pattern and never report the quad at all.

That is not a quirk of one implementation. It is why hidden quads almost never appear in solver logs, and why the honest advice is to look for the complement instead. Learning to see the quad is still worthwhile, because on paper the complement is sometimes the harder half to spot.

Worked example

The top-middle box has six empty cells and is missing 2, 4, 5, 6, 8 and 9. Track four of those digits. 2 fits only in r2c4 and r2c5. 4 fits only in r1c5 and r2c5. 9 fits only in r1c4 and r2c4. 5 fits in all four of those cells. Together, 2, 4, 5 and 9 reach exactly four cells, so the quad is confirmed.

Those cells therefore hold the four digits between them, and their other candidates go. r1c4 drops from 5, 6, 8, 9 to 5 and 9. r1c5 drops from 4, 5, 6, 8 to 4 and 5. r2c4 loses its 6 and keeps 2, 5 and 9. r2c5 loses its 6 and keeps 2, 4 and 5.

Look at what is left in the box: r3c4 and r3c5 both read 6 and 8. That naked pair is the complement of the quad and proves exactly the same thing in two cells instead of four. A solver working in difficulty order will always report the pair, which is why the board above had to be handed to the hidden quad detector directly to produce this diagram.

How to spot a hidden quad

1. Count the blanks in the unitNote how many empty cells the row, column or box still has. Anything from five to nine blanks can carry a hidden quad.
2. Check the complement firstSubtract four from the blank count. If the answer is two, three or four, look for a naked subset of that size instead. It is the same deduction and far quicker to confirm.
3. Otherwise list homes per digitFor each digit the unit still needs, write down the cells where it can go. Digits with two, three or four homes are quad material.
4. Find four digits covering four cellsCombine four home lists. If the union is exactly four cells, delete every other candidate from those cells and rescan the unit.

Common mistakes

• Searching for four digits that each fit in all four cells. That shape is possible but unusual; two or three homes per digit is the normal case.
• Missing a fifth home for one of the digits. A single stray cell anywhere in the unit destroys the pattern.
• Clearing the four digits from the rest of the unit. That is the naked version; a hidden quad cleans its own cells.
• Spending time on a quad when the unit has six blanks. The complementary naked pair is sitting right there and takes seconds to verify.