Hidden Pair

Level 3 · Yellow Belt

Strategy:

Requires:

Learn after:

Overview

A Hidden Pair occurs when two candidates appear in exactly two cells within a house, even though those cells may contain other candidates. Since those two digits must go in those two cells, all other candidates can be eliminated from them.

How It Works

Within a house, find two digits that appear as candidates in exactly the same two cells.
These two cells are the only places for those two digits within the house.
Eliminate all other candidates from those two cells, leaving only the pair.

Example

Starting position

Look for Hidden Pair.

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

1

Scan box 7 for 4 and 5

Check digits 4 and 5 in box 7.

Sudoku grid illustrating step 1: Scan box 7 for 4 and 5 — Check digits 4 and 5 in box 7.

2

r7c1 is already filled

r7c1 is already filled with 6.

Sudoku grid illustrating step 2: r7c1 is already filled — r7c1 is already filled with 6.

3

r9c1 is already filled

r9c1 is already filled with 8.

Sudoku grid illustrating step 3: r9c1 is already filled — r9c1 is already filled with 8.

4

4 is blocked from r7c3 by the column

Digit 4 cannot go in r7c3 because r5c3 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 4: 4 is blocked from r7c3 by the column — Digit 4 cannot go in r7c3 because r5c3 is already in this column. Remove the entry or choose a different digit.

5

4 was already removed from r8c1

Digit 4 is not a current candidate in r8c1 because earlier solving steps already removed it.

Sudoku grid illustrating step 5: 4 was already removed from r8c1 — Digit 4 is not a current candidate in r8c1 because earlier solving steps already removed it.

6

4 is blocked from r8c3 by the column

Digit 4 cannot go in r8c3 because r5c3 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 6: 4 is blocked from r8c3 by the column — Digit 4 cannot go in r8c3 because r5c3 is already in this column. Remove the entry or choose a different digit.

7

4 is blocked from r9c2 by the row

Digit 4 cannot go in r9c2 because r9c4 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 7: 4 is blocked from r9c2 by the row — Digit 4 cannot go in r9c2 because r9c4 is already in this row. Remove the entry or choose a different digit.

8

4 is blocked from r9c3 by row and column

Digit 4 cannot go in r9c3 because r9c4 is in this row and r5c3 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 8: 4 is blocked from r9c3 by row and column — Digit 4 cannot go in r9c3 because r9c4 is in this row and r5c3 is in this column. Remove the entry or choose a different digit.

9

5 is blocked from r7c3 by the column

Digit 5 cannot go in r7c3 because r6c3 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 9: 5 is blocked from r7c3 by the column — Digit 5 cannot go in r7c3 because r6c3 is already in this column. Remove the entry or choose a different digit.

10

5 is blocked from r8c1 by the column

Digit 5 cannot go in r8c1 because r1c1 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 10: 5 is blocked from r8c1 by the column — Digit 5 cannot go in r8c1 because r1c1 is already in this column. Remove the entry or choose a different digit.

11

5 is blocked from r8c3 by the column

Digit 5 cannot go in r8c3 because r6c3 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 11: 5 is blocked from r8c3 by the column — Digit 5 cannot go in r8c3 because r6c3 is already in this column. Remove the entry or choose a different digit.

12

5 is blocked from r9c2 by the row

Digit 5 cannot go in r9c2 because r9c6 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 12: 5 is blocked from r9c2 by the row — Digit 5 cannot go in r9c2 because r9c6 is already in this row. Remove the entry or choose a different digit.

13

5 is blocked from r9c3 by row and column

Digit 5 cannot go in r9c3 because r9c6 is in this row and r6c3 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 13: 5 is blocked from r9c3 by row and column — Digit 5 cannot go in r9c3 because r9c6 is in this row and r6c3 is in this column. Remove the entry or choose a different digit.

14

Two cells are reserved in the box

These two digits appear only in cells r7c2 and r8c2, so the box has reserved those cells for them.

Sudoku grid illustrating step 14: Two cells are reserved in the box — These two digits appear only in cells r7c2 and r8c2, so the box has reserved those cells for them.

15

Hidden Pair of 4 and 5

That means those two cells must end up as 4 and 5 in some order.

Sudoku grid illustrating step 15: Hidden Pair of 4 and 5 — That means those two cells must end up as 4 and 5 in some order.

16

Extra candidates in the pair cells

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

Sudoku grid illustrating step 16: Extra candidates in the pair cells — Any other candidates still written in those two cells are extra and must be removed.

17

Keep only 4 and 5

Remove every candidate except 4 and 5 from those two cells.

Sudoku grid illustrating step 17: Keep only 4 and 5 — Remove every candidate except 4 and 5 from those two cells.

18

Result

Result after applying the technique.

Sudoku grid showing the result after applying the technique

Tips & Patterns

Look for digits that appear rarely (2-3 times) within a house.
After finding a Hidden Pair, check if it creates Naked Singles.
Hidden Pairs are often easier to spot in blocks than in rows/columns.