Naked Quad
Four cells in a unit using only four candidates between them. Those digits are locked into those cells.
What it is
A naked quad follows the same logic as pairs and triples, one size larger: four cells whose combined candidates amount to exactly four digits. Those four digits must fill those four cells, so they can be removed from every other cell in the unit. Individual cells may show two, three or four of the digits.
How to spot it
Quads are easiest to find in units where only five or six cells remain empty, because then the quad is nearly the whole unit. Look for four cells whose candidates are drawn from a small pool of digits, and check whether the union is exactly four.
Worked example
Step through the reasoning below. Each step adds one layer: first the position, then the pattern, then the candidates involved, and finally what can be eliminated.
Step 1 of 4: The starting position
- Pattern cells
- 1/3, 2/3, 7/3, 8/3
- Digits
- 3, 4, 9, 1
- Eliminations
- 3/3, 4/3
Press a marked square to point it out on the board above.
Why it matters
Quads are uncommon, but when a unit is dense they can produce several eliminations at once. It is also worth knowing that a naked quad in a unit with five empty cells leaves the fifth cell as an immediate single.
Frequently asked questions
Are naked quads worth looking for?
Usually only on hard and expert puzzles, and mainly in units with few empty cells. Simpler techniques almost always come first.
Is there a shortcut for finding them?
Yes: if a unit has five empty cells and four of them share four digits, the fifth cell is immediately a naked single. Counting empty cells first saves time.
Put it to use
Where you will meet it
Hard grids are built around moves like this one. That is where it earns its keep.
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