Hidden Quad
Four digits fit only the same four cells in a unit.
A hidden quad is four candidate digits that between them can legally go in only four cells of a single row, column or box — even while those cells still display other candidates alongside them. Because those four digits are locked to those four cells, the hidden quad sudoku technique lets you strip away every other candidate crowding those cells. It is the four-digit relative of the hidden pair and hidden triple, and the exact mirror image of the naked quad.
Worked example
Scan row 1 for where the digits 1, 2, 3 and 4 can go: only the first four cells — R1C1={1,2,5}, R1C2={2,3,6}, R1C3={3,4,7} and R1C4={1,4,8}. Since no other cell in the row can take a 1, 2, 3 or 4, these four cells must hold those four digits between them. That leaves no room for the tag-along candidates, so the 5 in R1C1, the 6 in R1C2, the 7 in R1C3 and the 8 in R1C4 are all removed. Each of the four cells is reduced to its share of {1,2,3,4}.
When to use it
Reach for a hidden quad only after singles, pairs and triples have dried up and a unit is still congested with candidates. Rather than scanning cells, scan the unit's missing digits: pick four of them and check whether they are confined to the same four cells. If they are, every other candidate in those four cells can go. It is the hardest hidden subset to see, so count digit by digit and stay patient.
How to use it
- Track four digits. Find four digits in a unit whose possible positions fall within the same four cells.
- Confirm the hidden quad. Those four digits are locked to those four cells, no matter what other candidates are listed there.
- Clean the cells. Remove all other candidates from the four cells.
Frequently asked questions
What is a hidden quad in Sudoku?
A hidden quad is a set of four candidate digits that can only be placed in four cells of one unit, even though each of those cells still shows other candidates too. Because the four digits are pinned to those four cells, you can delete every other candidate from them. In the row-1 example, digits 1, 2, 3 and 4 are trapped in R1C1 through R1C4, so the tag-along 5, 6, 7 and 8 are cleared out.
How do I spot a hidden quad?
Don't scan cells — scan a unit's unsolved digits. List the digits still missing from a congested row, column or box and look for four of them that can only land in the same four cells. If exactly four digits are confined to exactly four cells, you have a hidden quad. It is the hardest hidden subset to see because the four digits are buried among other candidates, so it rewards patient, digit-by-digit counting.
What is the difference between a hidden quad and a naked quad?
They are mirror images of each other. A naked quad is four cells that contain only four digits between them, which lets you remove those digits from the rest of the unit. A hidden quad is four digits confined to four cells, which lets you remove the OTHER candidates from those four cells. Note that the four cells don't each need all four digits — only the four digits collectively must be locked to the four cells, as with 1, 2, 3 and 4 across R1C1 to R1C4.