Overview
- Tier 3
- Subsets
- Typical difficulty
- Peak Score 50–65
- Also known as
- Disjoint Quad, Naked Quadruple
When four cells in a house have candidates drawn strictly from four digits {A, B, C, D}, those four digits are locked into those four cells, eliminating them from the rest of the house.
Naked Quads represent the largest practical naked subset used in standard 9×9 Sudoku. Finding four cells whose candidate union contains exactly four digits requires keen observation. Interestingly, every Naked Quad in a house is mathematically complementary to a Hidden Pair in that same house, meaning if you find the quad, you could also have found the pair.
Worked examples
1 / 5
Reading the exampleCells forming the patternCells losing candidatesEliminated candidates
37
2
5
89
4
89
6
137
137
37
1
9
6
2
5
4
8
37
4
8
6
3
1
7
5
2
9
58
7
18
4
59
6
12389
1359
1235
9
6
3
18
58
2
7
15
4
2
45
148
7
3
19
189
159
6
56
345
24
189
89
189
23
34567
2357
68
49
248
5
7
3
129
1469
12
1
359
7
2
6
4
39
359
8
In column 8, R4C8, R5C8, R6C8 and R9C8 hold only {1,3,5,9} between them. Those four cells must take those four digits, so 1, 3, 5 and 9 can be removed from the rest of column 8.
Removes: 3 from R7C8, R1C8 · 5 from R7C8 · 9 from R8C8 · 1 from R8C8, R1C8
How to apply it
Spotting the pattern and making the deduction, in order.
- Look for four cells in the same unit whose pencil marks only contain four specific digits (e.g. 1, 4, 6, 9).
- Verify that none of the four cells contain any candidate outside that four-digit set.
- Because four slots must accommodate those four numbers, those digits are fully occupied by the group.
- Erase those four candidate digits from every other cell in that row, column, or box.
Common mistakes
- Missing cells with only 2 candidates that form part of the quad.
- Spending too much time searching for a quad when looking for its complementary Hidden Pair or Hidden Single would be much faster.
- Eliminating candidates from the quad cells themselves instead of from the remaining cells in the house.
Frequently asked questions
- Why are Naked Quads so rare in puzzles?
- Because most puzzles that have a Naked Quad can be solved faster by finding the complementary Hidden Pair or Hidden Triple in the remaining cells of that house.
- Can a Naked Quad consist entirely of pairs?
- Yes! For example, {1, 2}, {2, 3}, {3, 4}, and {1, 4} form a valid Naked Quad on digits {1, 2, 3, 4}.
Related techniques
Put Naked Quad into practice
Try a puzzle from the Hard tier (Peak Score 51–60).