Hidden Quad

Level 8 · Blue 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

Look for Hidden Quad.

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

1

Hidden Quad

Check digits 2, 6, 7 and 8 in box 5.

Sudoku grid illustrating step 1: Hidden Quad — Check digits 2, 6, 7 and 8 in box 5.

2

Hidden Quad

Digit 2 cannot go in r4c5 because r1c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 2: Hidden Quad — Digit 2 cannot go in r4c5 because r1c5 is already in this column. Remove the entry or choose a different digit.

3

Hidden Quad

Digit 2 cannot go in r5c5 because r1c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 3: Hidden Quad — Digit 2 cannot go in r5c5 because r1c5 is already in this column. Remove the entry or choose a different digit.

4

Hidden Quad

Digit 2 cannot go in r6c4 because r6c9 is in this row and r8c4 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 4: Hidden Quad — Digit 2 cannot go in r6c4 because r6c9 is in this row and r8c4 is in this column. Remove the entry or choose a different digit.

5

Hidden Quad

Digit 2 cannot go in r6c5 because r6c9 is in this row and r1c5 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 5: Hidden Quad — Digit 2 cannot go in r6c5 because r6c9 is in this row and r1c5 is in this column. Remove the entry or choose a different digit.

6

Hidden Quad

Digit 2 cannot go in r6c6 because r6c9 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 6: Hidden Quad — Digit 2 cannot go in r6c6 because r6c9 is already in this row. Remove the entry or choose a different digit.

7

Hidden Quad

Digit 6 cannot go in r4c5 because r3c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 7: Hidden Quad — Digit 6 cannot go in r4c5 because r3c5 is already in this column. Remove the entry or choose a different digit.

8

Hidden Quad

Digit 6 cannot go in r5c5 because r5c7 is in this row and r3c5 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 8: Hidden Quad — Digit 6 cannot go in r5c5 because r5c7 is in this row and r3c5 is in this column. Remove the entry or choose a different digit.

9

Hidden Quad

Digit 6 cannot go in r6c4 because r6c3 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 9: Hidden Quad — Digit 6 cannot go in r6c4 because r6c3 is already in this row. Remove the entry or choose a different digit.

10

Hidden Quad

Digit 6 cannot go in r6c5 because r6c3 is in this row and r3c5 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 10: Hidden Quad — Digit 6 cannot go in r6c5 because r6c3 is in this row and r3c5 is in this column. Remove the entry or choose a different digit.

11

Hidden Quad

Digit 6 cannot go in r6c6 because r6c3 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 11: Hidden Quad — Digit 6 cannot go in r6c6 because r6c3 is already in this row. Remove the entry or choose a different digit.

12

Hidden Quad

Digit 7 cannot go in r4c5 because r4c3 is in this row and r9c5 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 12: Hidden Quad — Digit 7 cannot go in r4c5 because r4c3 is in this row and r9c5 is in this column. Remove the entry or choose a different digit.

13

Hidden Quad

Digit 7 cannot go in r5c5 because r9c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 13: Hidden Quad — Digit 7 cannot go in r5c5 because r9c5 is already in this column. Remove the entry or choose a different digit.

14

Hidden Quad

Digit 7 cannot go in r6c4 because r6c7 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 14: Hidden Quad — Digit 7 cannot go in r6c4 because r6c7 is already in this row. Remove the entry or choose a different digit.

15

Hidden Quad

Digit 7 cannot go in r6c5 because r6c7 is in this row and r9c5 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 15: Hidden Quad — Digit 7 cannot go in r6c5 because r6c7 is in this row and r9c5 is in this column. Remove the entry or choose a different digit.

16

Hidden Quad

Digit 7 cannot go in r6c6 because r6c7 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 16: Hidden Quad — Digit 7 cannot go in r6c6 because r6c7 is already in this row. Remove the entry or choose a different digit.

17

Hidden Quad

Digit 8 cannot go in r4c5 because r2c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 17: Hidden Quad — Digit 8 cannot go in r4c5 because r2c5 is already in this column. Remove the entry or choose a different digit.

18

Hidden Quad

Digit 8 cannot go in r5c5 because r2c5 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 18: Hidden Quad — Digit 8 cannot go in r5c5 because r2c5 is already in this column. Remove the entry or choose a different digit.

19

Hidden Quad

Digit 8 cannot go in r6c4 because r6c1 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 19: Hidden Quad — Digit 8 cannot go in r6c4 because r6c1 is already in this row. Remove the entry or choose a different digit.

20

Hidden Quad

Digit 8 cannot go in r6c5 because r6c1 is in this row and r2c5 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 20: Hidden Quad — Digit 8 cannot go in r6c5 because r6c1 is in this row and r2c5 is in this column. Remove the entry or choose a different digit.

21

Hidden Quad

Digit 8 cannot go in r6c6 because r6c1 is in this row and r8c6 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 21: Hidden Quad — Digit 8 cannot go in r6c6 because r6c1 is in this row and r8c6 is in this column. Remove the entry or choose a different digit.

22

Hidden Quad

These 4 digits appear only in cells r4c4, r4c6, r5c4 and r5c6, so the box has reserved those cells for them.

Sudoku grid illustrating step 22: Hidden Quad — These 4 digits appear only in cells r4c4, r4c6, r5c4 and r5c6, so the box has reserved those cells for them.

23

Hidden Quad

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

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

24

Hidden Quad

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

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

25

Hidden Quad

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

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

26

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.