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Techniques › Naked Quad

Naked Quad

Four cells sharing four candidates between them. Rare, and usually preempted.

Four cells in a house whose candidates union to exactly four digits. The logic is identical to the pair and the triple, extended one more step.

Naked Quads are rare in practice, and not because the pattern is unusual: in a house with m empty cells, a naked quad implies a hidden (m−4)-set among the others, and the hidden form is very often simpler. Most quads are solved by something easier before you ever see them.

A worked example

Taken from a real puzzle in our bank, at the point where this was the cheapest move available. Pattern candidates are marked in amber; anything the step eliminates is struck through in red.

9 6 1 8 7 2 4 3 5
35 35 8 4 6 1 9 7 2
7 2 4 5 3 9 1 6 8
6 9 5 7 1 8 2 4 3
1 4 7 3 2 6 8 5 9
38 38 2 9 4 5 7 1 6
458 158 6 12 9 34 35 28 7
2 7 39 16 58 34 356 89 14
458 158 39 126 58 7 356 289 14
  1. NudgeA few cells in row 9 share the same small set of candidates between them.
  2. WhereNaked Quad in row 9: r9c1, r9c2, r9c5, r9c9
  3. Do itRemove r9c4 ≠ 1, r9c7 ≠ 5, r9c8 ≠ 8

How to spot it

Four cells with two to four candidates each whose union is four digits. Only worth hunting when a house has seven or more empty cells and nothing simpler applies.

Practise the Naked Quad →

Where you will meet it

Naked Quad sits at tier 2 of our ladder, which means it first becomes necessary at Medium. Puzzles below that band never require it, though it may still appear as a shortcut.

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