Naked Quads
Short answer: a naked quad is four cells in the same unit whose candidates, pooled together, come to exactly four shapes. Those four cells have to use up all four shapes between them, so none of the four can survive anywhere else in that unit. It is the same argument as a naked pair or triple, one size larger — and that extra size is exactly why it hides so well.
What a naked quad looks like
Naked quads rarely announce themselves. The four cells almost never show four candidates each — usually they show two or three, and no two of them look alike. What matters is not how many marks each cell carries but how many different shapes the four cells use in total.
Notice that no single cell in the quad holds all four shapes, and two of them hold only two. That is normal. A naked quad is a statement about the group, never about any one cell in it.
How to use a naked quad
- Pick a unit with few unsolved cells. Quads only pay off where six or more cells are still open, but they are easiest to see where the pencil marks are already thin. Scan a row, column or box at a time.
- Pool the candidates. Look at cells holding two, three or four marks and add up how many distinct shapes a group of four of them uses. You want exactly four shapes across exactly four cells.
- Check it is not really a triple. If three of the four cells already use only three shapes, you have a naked triple with a passenger, not a quad. Apply the triple instead — it is the stronger and simpler claim.
- Strike the four shapes elsewhere. Every other cell in that unit loses all four shapes. Those removals often expose a naked or hidden single immediately, which is usually where the real progress comes from.
Naked quads are the last of the subset techniques. If this one feels familiar, that is because it is: work back through naked pairs and naked triples and you will see the same sentence each time, with a different number in it.
Naked quads vs hidden quads
A naked quad is four cells that between them use only four shapes. A hidden quad is four shapes that between them fit in only four cells. They are mirror images, and both are present on any board where either one is — but you usually only see one of them, because a naked quad is easier to spot when the cells are sparse and a hidden quad is easier when they are crowded. In practice, if a unit has more empty cells than that, look for the hidden version first.
Find Naked Quads in your own grid
Paste a puzzle and this page will look for Naked Quads in it — the same pattern shown above, in your grid instead of ours. Nothing is uploaded; it runs in your browser.
Frequently asked questions
Are naked quads worth learning, or are they too rare?
They are genuinely rare, and many solvers finish hard puzzles without ever needing one. Learn them anyway for the pattern rather than the frequency: once you can see a quad, the pairs and triples you already know become much faster to spot, because you stop reading cells one at a time and start reading groups.
Do all four cells need four candidates each?
No — and they almost never do. Each cell needs at least two candidates and no more than four, and all four cells together must use exactly four distinct shapes. A quad made of cells showing two, three, two and three marks is completely normal.
What if only three of the four cells use three shapes?
Then it is a naked triple, not a quad, and the fourth cell is just along for the ride. Apply the triple — it removes those three shapes from the fourth cell too, which usually solves it outright. A "quad" that is really a triple is the most common mistake here.
Does this work in normal number sudoku?
Yes, identically. Sudoku involves no arithmetic, so the digits 1–9 are just nine tokens. A naked quad of 2, 5, 7 and 9 behaves exactly like one of circle, square, triangle and heart. Learning it with shapes just keeps the logic visible.