Hidden Quad

Level 9 · Purple Belt

Strategy:

Requires:

Overview

A Hidden Quad is the four-cell extension of Hidden Pairs and Triples. When four candidates appear exclusively in four cells within a house, all other candidates can be eliminated from those cells.

How It Works

Within a house, identify four digits that appear only within the same four cells.
These four cells must contain these four digits.
Eliminate all other candidates from these four cells.

Example

Starting position

Look for Hidden Quad.

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

1

Scan row 3 for 2, 3, 6 and 9

Check digits 2, 3, 6 and 9 in row 3.

Sudoku grid illustrating step 1: Scan row 3 for 2, 3, 6 and 9 — Check digits 2, 3, 6 and 9 in row 3.

2

2 is blocked from r3c4 by the column

Digit 2 cannot go in r3c4 because r1c4 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 2: 2 is blocked from r3c4 by the column — Digit 2 cannot go in r3c4 because r1c4 is already in this column. Remove the entry or choose a different digit.

3

2 is blocked from r3c5 by the box

Digit 2 cannot go in r3c5 because r1c4 is already in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 3: 2 is blocked from r3c5 by the box — Digit 2 cannot go in r3c5 because r1c4 is already in this box. Remove the entry or choose a different digit.

4

2 is blocked from r3c7 by column and box

Digit 2 cannot go in r3c7 because r7c7 is in this column and r2c9 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 4: 2 is blocked from r3c7 by column and box — Digit 2 cannot go in r3c7 because r7c7 is in this column and r2c9 is in this box. Remove the entry or choose a different digit.

5

2 is blocked from r3c8 by the box

Digit 2 cannot go in r3c8 because r2c9 is already in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 5: 2 is blocked from r3c8 by the box — Digit 2 cannot go in r3c8 because r2c9 is already in this box. Remove the entry or choose a different digit.

6

2 is blocked from r3c9 by the column

Digit 2 cannot go in r3c9 because r2c9 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 6: 2 is blocked from r3c9 by the column — Digit 2 cannot go in r3c9 because r2c9 is already in this column. Remove the entry or choose a different digit.

7

3 is blocked from r3c4 by column and box

Digit 3 cannot go in r3c4 because r6c4 is in this column and r1c5 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 7: 3 is blocked from r3c4 by column and box — Digit 3 cannot go in r3c4 because r6c4 is in this column and r1c5 is in this box. Remove the entry or choose a different digit.

8

3 is blocked from r3c5 by the column

Digit 3 cannot go in r3c5 because r1c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 8: 3 is blocked from r3c5 by the column — Digit 3 cannot go in r3c5 because r1c5 is already in this column. Remove the entry or choose a different digit.

9

3 is blocked from r3c7 by the column

Digit 3 cannot go in r3c7 because r2c7 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 9: 3 is blocked from r3c7 by the column — Digit 3 cannot go in r3c7 because r2c7 is already in this column. Remove the entry or choose a different digit.

10

3 is blocked from r3c8 by the box

Digit 3 cannot go in r3c8 because r2c7 is already in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 10: 3 is blocked from r3c8 by the box — Digit 3 cannot go in r3c8 because r2c7 is already in this box. Remove the entry or choose a different digit.

11

3 is blocked from r3c9 by column and box

Digit 3 cannot go in r3c9 because r8c9 is in this column and r2c7 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 11: 3 is blocked from r3c9 by column and box — Digit 3 cannot go in r3c9 because r8c9 is in this column and r2c7 is in this box. Remove the entry or choose a different digit.

12

6 is blocked from r3c4 by the column

Digit 6 cannot go in r3c4 because r9c4 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 12: 6 is blocked from r3c4 by the column — Digit 6 cannot go in r3c4 because r9c4 is already in this column. Remove the entry or choose a different digit.

13

6 is blocked from r3c5 by the column

Digit 6 cannot go in r3c5 because r5c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 13: 6 is blocked from r3c5 by the column — Digit 6 cannot go in r3c5 because r5c5 is already in this column. Remove the entry or choose a different digit.

14

6 is blocked from r3c7 by the column

Digit 6 cannot go in r3c7 because r1c7 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 14: 6 is blocked from r3c7 by the column — Digit 6 cannot go in r3c7 because r1c7 is already in this column. Remove the entry or choose a different digit.

15

6 is blocked from r3c8 by column and box

Digit 6 cannot go in r3c8 because r7c8 is in this column and r1c7 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 15: 6 is blocked from r3c8 by column and box — Digit 6 cannot go in r3c8 because r7c8 is in this column and r1c7 is in this box. Remove the entry or choose a different digit.

16

6 is blocked from r3c9 by column and box

Digit 6 cannot go in r3c9 because r4c9 is in this column and r1c7 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 16: 6 is blocked from r3c9 by column and box — Digit 6 cannot go in r3c9 because r4c9 is in this column and r1c7 is in this box. Remove the entry or choose a different digit.

17

9 is blocked from r3c4 by the column

Digit 9 cannot go in r3c4 because r7c4 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 17: 9 is blocked from r3c4 by the column — Digit 9 cannot go in r3c4 because r7c4 is already in this column. Remove the entry or choose a different digit.

18

9 is blocked from r3c5 by the column

Digit 9 cannot go in r3c5 because r4c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 18: 9 is blocked from r3c5 by the column — Digit 9 cannot go in r3c5 because r4c5 is already in this column. Remove the entry or choose a different digit.

19

9 is blocked from r3c7 by the box

Digit 9 cannot go in r3c7 because r2c8 is already in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 19: 9 is blocked from r3c7 by the box — Digit 9 cannot go in r3c7 because r2c8 is already in this box. Remove the entry or choose a different digit.

20

9 is blocked from r3c8 by the column

Digit 9 cannot go in r3c8 because r2c8 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 20: 9 is blocked from r3c8 by the column — Digit 9 cannot go in r3c8 because r2c8 is already in this column. Remove the entry or choose a different digit.

21

9 is blocked from r3c9 by the box

Digit 9 cannot go in r3c9 because r2c8 is already in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 21: 9 is blocked from r3c9 by the box — Digit 9 cannot go in r3c9 because r2c8 is already in this box. Remove the entry or choose a different digit.

22

Four cells are reserved in the row

These 4 digits appear only in columns 1, 2, 3 and 6, so row 3 has reserved those cells for them.

Sudoku grid illustrating step 22: Four cells are reserved in the row — These 4 digits appear only in columns 1, 2, 3 and 6, so row 3 has reserved those cells for them.

23

Hidden Quad in those cells

Those cells must contain these hidden quad digits in some order.

Sudoku grid illustrating step 23: Hidden Quad in those cells — Those cells must contain these hidden quad digits in some order.

24

Extra candidates in the quad cells

Any other candidates still written in those cells are extra and must be removed.

Sudoku grid illustrating step 24: Extra candidates in the quad cells — Any other candidates still written in those cells are extra and must be removed.

25

Keep only the quad digits

Remove every candidate that is not part of the hidden quad from those cells.

Sudoku grid illustrating step 25: Keep only the quad digits — Remove every candidate that is not part of the hidden quad from those cells.

26

Result

Result after applying the technique.

Sudoku grid showing the result after applying the technique

Tips & Patterns

Hidden Quads are quite rare - don't spend too much time looking initially.
They often appear in puzzles designed to require advanced techniques.
Software or systematic checking helps identify them reliably.