Naked Quad

Level 9 · Purple 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

Starting position

Look for Naked Quad.

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

1

Scan box 8 for a quad

Check cells r7c4, r8c4, r9c4 and r9c6 in box 8.

Sudoku grid illustrating step 1: Scan box 8 for a quad — Check cells r7c4, r8c4, r9c4 and r9c6 in box 8.

2

1 is blocked from r7c4 by the row

Digit 1 cannot go in r7c4 because r7c8 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 2: 1 is blocked from r7c4 by the row — Digit 1 cannot go in r7c4 because r7c8 is already in this row. Remove the entry or choose a different digit.

3

3 is blocked from r7c4 by row, column and box

Digit 3 cannot go in r7c4 because r7c9 is in this row, r6c4 is in this column, and r8c6 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 3: 3 is blocked from r7c4 by row, column and box — Digit 3 cannot go in r7c4 because r7c9 is in this row, r6c4 is in this column, and r8c6 is in this box. Remove the entry or choose a different digit.

4

4 is blocked from r7c4 by column and box

Digit 4 cannot go in r7c4 because r4c4 is in this column and r9c5 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 4: 4 is blocked from r7c4 by column and box — Digit 4 cannot go in r7c4 because r4c4 is in this column and r9c5 is in this box. Remove the entry or choose a different digit.

5

5 is blocked from r7c4 by the column

Digit 5 cannot go in r7c4 because r5c4 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 5: 5 is blocked from r7c4 by the column — Digit 5 cannot go in r7c4 because r5c4 is already in this column. Remove the entry or choose a different digit.

6

6 is blocked from r7c4 by the column

Digit 6 cannot go in r7c4 because r2c4 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 6: 6 is blocked from r7c4 by the column — Digit 6 cannot go in r7c4 because r2c4 is already in this column. Remove the entry or choose a different digit.

7

8 is blocked from r7c4 by row and column

Digit 8 cannot go in r7c4 because r7c5 is in this row and r3c4 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 7: 8 is blocked from r7c4 by row and column — Digit 8 cannot go in r7c4 because r7c5 is in this row and r3c4 is in this column. Remove the entry or choose a different digit.

8

2 is blocked from r8c4 by the row

Digit 2 cannot go in r8c4 because r8c7 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 8: 2 is blocked from r8c4 by the row — Digit 2 cannot go in r8c4 because r8c7 is already in this row. Remove the entry or choose a different digit.

9

3 is blocked from r8c4 by row and column

Digit 3 cannot go in r8c4 because r8c6 is in this row and r6c4 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 9: 3 is blocked from r8c4 by row and column — Digit 3 cannot go in r8c4 because r8c6 is in this row and r6c4 is in this column. Remove the entry or choose a different digit.

10

4 is blocked from r8c4 by column and box

Digit 4 cannot go in r8c4 because r4c4 is in this column and r9c5 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 10: 4 is blocked from r8c4 by column and box — Digit 4 cannot go in r8c4 because r4c4 is in this column and r9c5 is in this box. Remove the entry or choose a different digit.

11

5 is blocked from r8c4 by the column

Digit 5 cannot go in r8c4 because r5c4 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 11: 5 is blocked from r8c4 by the column — Digit 5 cannot go in r8c4 because r5c4 is already in this column. Remove the entry or choose a different digit.

12

6 is blocked from r8c4 by the column

Digit 6 cannot go in r8c4 because r2c4 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 12: 6 is blocked from r8c4 by the column — Digit 6 cannot go in r8c4 because r2c4 is already in this column. Remove the entry or choose a different digit.

13

8 is blocked from r8c4 by column and box

Digit 8 cannot go in r8c4 because r3c4 is in this column and r7c5 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 13: 8 is blocked from r8c4 by column and box — Digit 8 cannot go in r8c4 because r3c4 is in this column and r7c5 is in this box. Remove the entry or choose a different digit.

14

9 is blocked from r8c4 by the row

Digit 9 cannot go in r8c4 because r8c8 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 14: 9 is blocked from r8c4 by the row — Digit 9 cannot go in r8c4 because r8c8 is already in this row. Remove the entry or choose a different digit.

15

3 is blocked from r9c4 by row, column and box

Digit 3 cannot go in r9c4 because r9c3 is in this row, r6c4 is in this column, and r8c6 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 15: 3 is blocked from r9c4 by row, column and box — Digit 3 cannot go in r9c4 because r9c3 is in this row, r6c4 is in this column, and r8c6 is in this box. Remove the entry or choose a different digit.

16

4 is blocked from r9c4 by row and column

Digit 4 cannot go in r9c4 because r9c5 is in this row and r4c4 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 16: 4 is blocked from r9c4 by row and column — Digit 4 cannot go in r9c4 because r9c5 is in this row and r4c4 is in this column. Remove the entry or choose a different digit.

17

5 is blocked from r9c4 by row and column

Digit 5 cannot go in r9c4 because r9c8 is in this row and r5c4 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 17: 5 is blocked from r9c4 by row and column — Digit 5 cannot go in r9c4 because r9c8 is in this row and r5c4 is in this column. Remove the entry or choose a different digit.

18

6 is blocked from r9c4 by row and column

Digit 6 cannot go in r9c4 because r9c7 is in this row and r2c4 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 18: 6 is blocked from r9c4 by row and column — Digit 6 cannot go in r9c4 because r9c7 is in this row and r2c4 is in this column. Remove the entry or choose a different digit.

19

8 is blocked from r9c4 by row, column and box

Digit 8 cannot go in r9c4 because r9c9 is in this row, r3c4 is in this column, and r7c5 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 19: 8 is blocked from r9c4 by row, column and box — Digit 8 cannot go in r9c4 because r9c9 is in this row, r3c4 is in this column, and r7c5 is in this box. Remove the entry or choose a different digit.

20

3 is blocked from r9c6 by row and column

Digit 3 cannot go in r9c6 because r9c3 is in this row and r8c6 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 20: 3 is blocked from r9c6 by row and column — Digit 3 cannot go in r9c6 because r9c3 is in this row and r8c6 is in this column. Remove the entry or choose a different digit.

21

4 is blocked from r9c6 by the row

Digit 4 cannot go in r9c6 because r9c5 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 21: 4 is blocked from r9c6 by the row — Digit 4 cannot go in r9c6 because r9c5 is already in this row. Remove the entry or choose a different digit.

22

5 is blocked from r9c6 by the row

Digit 5 cannot go in r9c6 because r9c8 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 22: 5 is blocked from r9c6 by the row — Digit 5 cannot go in r9c6 because r9c8 is already in this row. Remove the entry or choose a different digit.

23

6 is blocked from r9c6 by the row

Digit 6 cannot go in r9c6 because r9c7 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 23: 6 is blocked from r9c6 by the row — Digit 6 cannot go in r9c6 because r9c7 is already in this row. Remove the entry or choose a different digit.

24

7 is blocked from r9c6 by the column

Digit 7 cannot go in r9c6 because r5c6 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 24: 7 is blocked from r9c6 by the column — Digit 7 cannot go in r9c6 because r5c6 is already in this column. Remove the entry or choose a different digit.

25

8 is blocked from r9c6 by row, column and box

Digit 8 cannot go in r9c6 because r9c9 is in this row, r6c6 is in this column, and r7c5 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 25: 8 is blocked from r9c6 by row, column and box — Digit 8 cannot go in r9c6 because r9c9 is in this row, r6c6 is in this column, and r7c5 is in this box. Remove the entry or choose a different digit.

26

Four cells hold only 1, 2, 7 and 9

These 4 cells contain only candidates 1, 2, 7 and 9 and nothing else.

Sudoku grid illustrating step 26: Four cells hold only 1, 2, 7 and 9 — These 4 cells contain only candidates 1, 2, 7 and 9 and nothing else.

27

Digits 1, 2, 7 and 9 are locked in the quad

Because these cells must take the four digits 1, 2, 7 and 9 among themselves, no other cell in the box can keep them.

Sudoku grid illustrating step 27: Digits 1, 2, 7 and 9 are locked in the quad — Because these cells must take the four digits 1, 2, 7 and 9 among themselves, no other cell in the box can keep them.

28

Other cells in box 8 hold 1, 2, 7 and 9

Other cells in box 8 still contain 1, 2, 7 and 9 and are removal targets.

Sudoku grid illustrating step 28: Other cells in box 8 hold 1, 2, 7 and 9 — Other cells in box 8 still contain 1, 2, 7 and 9 and are removal targets.

29

Remove 1, 2, 7 and 9 from box 8

Remove 1, 2, 7 and 9 from the other cells in box 8.

Sudoku grid illustrating step 29: Remove 1, 2, 7 and 9 from box 8 — Remove 1, 2, 7 and 9 from the other cells in box 8.

30

Result

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.