Hidden Triple

Level 8 · Blue Belt

Strategy:

Requires:

Learn after:

Overview

A Hidden Triple extends the Hidden Pair concept to three cells and three candidates. When three candidates appear only in three cells within a house, all other candidates can be eliminated from those cells.

How It Works

Within a house, find three digits that appear only in the same three cells.
Those three cells must contain those three digits.
Eliminate all other candidates from those three cells.

Example

Starting position

Look for Hidden Triple.

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

1

Scan column 1 for 1, 8 and 9

Check digits 1, 8 and 9 in column 1.

Sudoku grid illustrating step 1: Scan column 1 for 1, 8 and 9 — Check digits 1, 8 and 9 in column 1.

2

r3c1 is already filled

r3c1 is already filled with 5.

Sudoku grid illustrating step 2: r3c1 is already filled — r3c1 is already filled with 5.

3

r7c1 is already filled

r7c1 is already filled with 3.

Sudoku grid illustrating step 3: r7c1 is already filled — r7c1 is already filled with 3.

4

1 is blocked from r4c1 by the box

Digit 1 cannot go in r4c1 because r6c3 is already in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 4: 1 is blocked from r4c1 by the box — Digit 1 cannot go in r4c1 because r6c3 is already in this box. Remove the entry or choose a different digit.

5

1 is blocked from r5c1 by the box

Digit 1 cannot go in r5c1 because r6c3 is already in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 5: 1 is blocked from r5c1 by the box — Digit 1 cannot go in r5c1 because r6c3 is already in this box. Remove the entry or choose a different digit.

6

1 is blocked from r6c1 by the row

Digit 1 cannot go in r6c1 because r6c3 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 6: 1 is blocked from r6c1 by the row — Digit 1 cannot go in r6c1 because r6c3 is already in this row. Remove the entry or choose a different digit.

7

1 is blocked from r8c1 by row and box

Digit 1 cannot go in r8c1 because r8c6 is in this row and r7c2 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 7: 1 is blocked from r8c1 by row and box — Digit 1 cannot go in r8c1 because r8c6 is in this row and r7c2 is in this box. Remove the entry or choose a different digit.

8

8 is blocked from r4c1 by the row

Digit 8 cannot go in r4c1 because r4c2 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 8: 8 is blocked from r4c1 by the row — Digit 8 cannot go in r4c1 because r4c2 is already in this row. Remove the entry or choose a different digit.

9

8 is blocked from r5c1 by row and box

Digit 8 cannot go in r5c1 because r5c6 is in this row and r4c2 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 9: 8 is blocked from r5c1 by row and box — Digit 8 cannot go in r5c1 because r5c6 is in this row and r4c2 is in this box. Remove the entry or choose a different digit.

10

8 is blocked from r6c1 by the box

Digit 8 cannot go in r6c1 because r4c2 is already in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 10: 8 is blocked from r6c1 by the box — Digit 8 cannot go in r6c1 because r4c2 is already in this box. Remove the entry or choose a different digit.

11

8 is blocked from r8c1 by the row

Digit 8 cannot go in r8c1 because r8c8 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 11: 8 is blocked from r8c1 by the row — Digit 8 cannot go in r8c1 because r8c8 is already in this row. Remove the entry or choose a different digit.

12

9 is blocked from r4c1 by the row

Digit 9 cannot go in r4c1 because r4c6 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 12: 9 is blocked from r4c1 by the row — Digit 9 cannot go in r4c1 because r4c6 is already in this row. Remove the entry or choose a different digit.

13

9 is blocked from r5c1 by the row

Digit 9 cannot go in r5c1 because r5c8 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 13: 9 is blocked from r5c1 by the row — Digit 9 cannot go in r5c1 because r5c8 is already in this row. Remove the entry or choose a different digit.

14

9 was already removed from r6c1

Digit 9 is not a current candidate in r6c1 because earlier solving steps already removed it.

Sudoku grid illustrating step 14: 9 was already removed from r6c1 — Digit 9 is not a current candidate in r6c1 because earlier solving steps already removed it.

15

9 is blocked from r8c1 by the row

Digit 9 cannot go in r8c1 because r8c4 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 15: 9 is blocked from r8c1 by the row — Digit 9 cannot go in r8c1 because r8c4 is already in this row. Remove the entry or choose a different digit.

16

Three cells are reserved in the column

These 3 digits appear only in rows 1, 2 and 9, so column 1 has reserved those cells for them.

Sudoku grid illustrating step 16: Three cells are reserved in the column — These 3 digits appear only in rows 1, 2 and 9, so column 1 has reserved those cells for them.

17

Hidden Triple in those cells

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

Sudoku grid illustrating step 17: Hidden Triple in those cells — Those cells must contain these hidden triple digits in some order.

18

Extra candidates in the triple cells

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

Sudoku grid illustrating step 18: Extra candidates in the triple cells — Any other candidates still written in those cells are extra and must be removed.

19

Keep only the triple digits

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

Sudoku grid illustrating step 19: Keep only the triple digits — Remove every candidate that is not part of the hidden triple from those cells.

20

Result

Result after applying the technique.

Sudoku grid showing the result after applying the technique

Tips & Patterns

Hidden Triples are harder to spot than Hidden Pairs - look for three rarely-occurring digits.
Not all three cells need to contain all three candidates.
Use a systematic approach: check each combination of three digits.