Hidden Triple

Level 4 · Yellow Belt (Orange Stripe)

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

Look for Hidden Triple.

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

1

Hidden Triple

Check digits 2, 7 and 8 in column 2.

Sudoku grid illustrating step 1: Hidden Triple — Check digits 2, 7 and 8 in column 2.

2

Hidden Triple

r1c2 is already filled with 9.

Sudoku grid illustrating step 2: Hidden Triple — r1c2 is already filled with 9.

3

Hidden Triple

r4c2 is already filled with 5.

Sudoku grid illustrating step 3: Hidden Triple — r4c2 is already filled with 5.

4

Hidden Triple

Digit 2 is not a current candidate in r2c2 because earlier solving steps already removed it.

Sudoku grid illustrating step 4: Hidden Triple — Digit 2 is not a current candidate in r2c2 because earlier solving steps already removed it.

5

Hidden Triple

Digit 2 is not a current candidate in r6c2 because earlier solving steps already removed it.

Sudoku grid illustrating step 5: Hidden Triple — Digit 2 is not a current candidate in r6c2 because earlier solving steps already removed it.

6

Hidden Triple

Digit 2 cannot go in r7c2 because r7c1 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 6: Hidden Triple — Digit 2 cannot go in r7c2 because r7c1 is already in this row. Remove the entry or choose a different digit.

7

Hidden Triple

Digit 2 cannot go in r8c2 because r7c1 is already in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 7: Hidden Triple — Digit 2 cannot go in r8c2 because r7c1 is already in this box. Remove the entry or choose a different digit.

8

Hidden Triple

Digit 7 cannot go in r2c2 because r2c7 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 8: Hidden Triple — Digit 7 cannot go in r2c2 because r2c7 is already in this row. Remove the entry or choose a different digit.

9

Hidden Triple

Digit 7 cannot go in r6c2 because r6c8 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 9: Hidden Triple — Digit 7 cannot go in r6c2 because r6c8 is already in this row. Remove the entry or choose a different digit.

10

Hidden Triple

Digit 7 cannot go in r7c2 because r7c9 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 10: Hidden Triple — Digit 7 cannot go in r7c2 because r7c9 is already in this row. Remove the entry or choose a different digit.

11

Hidden Triple

Digit 7 cannot go in r8c2 because r8c5 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 11: Hidden Triple — Digit 7 cannot go in r8c2 because r8c5 is already in this row. Remove the entry or choose a different digit.

12

Hidden Triple

Digit 8 cannot go in r2c2 because r2c1 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 12: Hidden Triple — Digit 8 cannot go in r2c2 because r2c1 is already in this row. Remove the entry or choose a different digit.

13

Hidden Triple

Digit 8 cannot go in r6c2 because r6c9 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 13: Hidden Triple — Digit 8 cannot go in r6c2 because r6c9 is already in this row. Remove the entry or choose a different digit.

14

Hidden Triple

Digit 8 cannot go in r7c2 because r7c4 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 14: Hidden Triple — Digit 8 cannot go in r7c2 because r7c4 is already in this row. Remove the entry or choose a different digit.

15

Hidden Triple

Digit 8 cannot go in r8c2 because r8c7 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 15: Hidden Triple — Digit 8 cannot go in r8c2 because r8c7 is already in this row. Remove the entry or choose a different digit.

16

Hidden Triple

These 3 digits appear only in rows 3, 5 and 9, so column 2 has reserved those cells for them.

Sudoku grid illustrating step 16: Hidden Triple — These 3 digits appear only in rows 3, 5 and 9, so column 2 has reserved those cells for them.

17

Hidden Triple

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

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

18

Hidden Triple

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

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

19

Hidden Triple

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

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

20

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.