Naked Quad

Level 5 · Orange Belt

Strategy:

Requires:

Overview

A Naked Quad consists of four cells in a house that together contain exactly four candidates. These four digits must occupy these four cells, allowing elimination from other cells.

How It Works

Find four cells in a house whose combined candidates total exactly four digits.
Each cell must contain only subsets of these four candidates.
Eliminate these four candidates from all other cells in the house.

Example

Look for Naked Quad.

Sudoku grid showing the initial puzzle state for Look for Naked Quad.

1

Naked Quad

Check cells r4c4, r4c5, r5c5 and r6c5 in box 5.

Sudoku grid illustrating step 1: Naked Quad — Check cells r4c4, r4c5, r5c5 and r6c5 in box 5.

2

Naked Quad

Digit 1 cannot go in r4c4 because r4c2 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 2: Naked Quad — Digit 1 cannot go in r4c4 because r4c2 is already in this row. Remove the entry or choose a different digit.

3

Naked Quad

Digit 3 cannot go in r4c4 because r7c4 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 3: Naked Quad — Digit 3 cannot go in r4c4 because r7c4 is already in this column. Remove the entry or choose a different digit.

4

Naked Quad

Digit 5 cannot go in r4c4 because r4c7 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 4: Naked Quad — Digit 5 cannot go in r4c4 because r4c7 is already in this row. Remove the entry or choose a different digit.

5

Naked Quad

Digit 6 cannot go in r4c4 because r4c1 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 5: Naked Quad — Digit 6 cannot go in r4c4 because r4c1 is already in this row. Remove the entry or choose a different digit.

6

Naked Quad

Digit 7 cannot go in r4c4 because r4c9 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 6: Naked Quad — Digit 7 cannot go in r4c4 because r4c9 is already in this row. Remove the entry or choose a different digit.

7

Naked Quad

Digit 8 cannot go in r4c4 because r9c4 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 7: Naked Quad — Digit 8 cannot go in r4c4 because r9c4 is already in this column. Remove the entry or choose a different digit.

8

Naked Quad

Digit 9 cannot go in r4c4 because r3c4 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 8: Naked Quad — Digit 9 cannot go in r4c4 because r3c4 is already in this column. Remove the entry or choose a different digit.

9

Naked Quad

Digit 1 cannot go in r4c5 because r4c2 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 9: Naked Quad — Digit 1 cannot go in r4c5 because r4c2 is already in this row. Remove the entry or choose a different digit.

10

Naked Quad

Digit 3 cannot go in r4c5 because r1c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 10: Naked Quad — Digit 3 cannot go in r4c5 because r1c5 is already in this column. Remove the entry or choose a different digit.

11

Naked Quad

Digit 5 cannot go in r4c5 because r4c7 is in this row and r2c5 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 11: Naked Quad — Digit 5 cannot go in r4c5 because r4c7 is in this row and r2c5 is in this column. Remove the entry or choose a different digit.

12

Naked Quad

Digit 6 cannot go in r4c5 because r4c1 is in this row and r9c5 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 12: Naked Quad — Digit 6 cannot go in r4c5 because r4c1 is in this row and r9c5 is in this column. Remove the entry or choose a different digit.

13

Naked Quad

Digit 7 cannot go in r4c5 because r4c9 is in this row and r7c5 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 13: Naked Quad — Digit 7 cannot go in r4c5 because r4c9 is in this row and r7c5 is in this column. Remove the entry or choose a different digit.

14

Naked Quad

Digit 9 cannot go in r4c5 because r8c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 14: Naked Quad — Digit 9 cannot go in r4c5 because r8c5 is already in this column. Remove the entry or choose a different digit.

15

Naked Quad

Digit 2 cannot go in r5c5 because r5c8 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 15: Naked Quad — Digit 2 cannot go in r5c5 because r5c8 is already in this row. Remove the entry or choose a different digit.

16

Naked Quad

Digit 3 cannot go in r5c5 because r1c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 16: Naked Quad — Digit 3 cannot go in r5c5 because r1c5 is already in this column. Remove the entry or choose a different digit.

17

Naked Quad

Digit 5 cannot go in r5c5 because r5c1 is in this row and r2c5 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 17: Naked Quad — Digit 5 cannot go in r5c5 because r5c1 is in this row and r2c5 is in this column. Remove the entry or choose a different digit.

18

Naked Quad

Digit 6 cannot go in r5c5 because r9c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 18: Naked Quad — Digit 6 cannot go in r5c5 because r9c5 is already in this column. Remove the entry or choose a different digit.

19

Naked Quad

Digit 7 cannot go in r5c5 because r7c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 19: Naked Quad — Digit 7 cannot go in r5c5 because r7c5 is already in this column. Remove the entry or choose a different digit.

20

Naked Quad

Digit 8 cannot go in r5c5 because r5c2 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 20: Naked Quad — Digit 8 cannot go in r5c5 because r5c2 is already in this row. Remove the entry or choose a different digit.

21

Naked Quad

Digit 9 cannot go in r5c5 because r8c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 21: Naked Quad — Digit 9 cannot go in r5c5 because r8c5 is already in this column. Remove the entry or choose a different digit.

22

Naked Quad

Digit 3 cannot go in r6c5 because r1c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 22: Naked Quad — Digit 3 cannot go in r6c5 because r1c5 is already in this column. Remove the entry or choose a different digit.

23

Naked Quad

Digit 4 cannot go in r6c5 because r6c3 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 23: Naked Quad — Digit 4 cannot go in r6c5 because r6c3 is already in this row. Remove the entry or choose a different digit.

24

Naked Quad

Digit 5 cannot go in r6c5 because r2c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 24: Naked Quad — Digit 5 cannot go in r6c5 because r2c5 is already in this column. Remove the entry or choose a different digit.

25

Naked Quad

Digit 6 cannot go in r6c5 because r6c8 is in this row and r9c5 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 25: Naked Quad — Digit 6 cannot go in r6c5 because r6c8 is in this row and r9c5 is in this column. Remove the entry or choose a different digit.

26

Naked Quad

Digit 7 cannot go in r6c5 because r7c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 26: Naked Quad — Digit 7 cannot go in r6c5 because r7c5 is already in this column. Remove the entry or choose a different digit.

27

Naked Quad

Digit 9 cannot go in r6c5 because r6c1 is in this row and r8c5 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 27: Naked Quad — Digit 9 cannot go in r6c5 because r6c1 is in this row and r8c5 is in this column. Remove the entry or choose a different digit.

28

Naked Quad

These 4 cells contain only candidates 1, 2, 4 and 8 and nothing else.

Sudoku grid illustrating step 28: Naked Quad — These 4 cells contain only candidates 1, 2, 4 and 8 and nothing else.

29

Naked Quad

Because these cells must take the four digits 1, 2, 4 and 8 among themselves, no other cell in the box can keep them.

Sudoku grid illustrating step 29: Naked Quad — Because these cells must take the four digits 1, 2, 4 and 8 among themselves, no other cell in the box can keep them.

30

Naked Quad

These are the other cells in box 5 that still contain 1, 2, 4 and 8 and must be cleaned up.

Sudoku grid illustrating step 30: Naked Quad — These are the other cells in box 5 that still contain 1, 2, 4 and 8 and must be cleaned up.

31

Naked Quad

Remove 1, 2, 4 and 8 from the other cells in box 5.

Sudoku grid illustrating step 31: Naked Quad — Remove 1, 2, 4 and 8 from the other cells in box 5.

32

Result after applying the technique.

Sudoku grid showing the result after applying the technique

Tips & Patterns

Naked Quads are uncommon but not as rare as Hidden Quads.
Look for groups of cells with 2-4 candidates that only use four digits combined.
Quads are harder to spot visually - use pencilmark highlighting if available.