Naked Triple

Level 4 · Yellow Belt (Orange Stripe)

Strategy:

Requires:

Learn after:

Overview

A Naked Triple consists of three cells in a house that together contain exactly three candidates. These three digits must go in these three cells, so they can be eliminated elsewhere in the house.

How It Works

Find three cells in a house where the union of their candidates contains exactly three digits.
Each cell must have a subset of these three candidates (2 or 3 of them).
Eliminate these three candidates from all other cells in the house.

Example

Look for Naked Triple.

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

1

Naked Triple

Check cells r7c8, r8c8 and r9c9 in box 9.

Sudoku grid illustrating step 1: Naked Triple — Check cells r7c8, r8c8 and r9c9 in box 9.

2

Naked Triple

Digit 1 cannot go in r7c8 because r1c8 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 2: Naked Triple — Digit 1 cannot go in r7c8 because r1c8 is already in this column. Remove the entry or choose a different digit.

3

Naked Triple

Digit 2 cannot go in r7c8 because r7c3 is in this row, r5c8 is in this column, and r9c7 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 3: Naked Triple — Digit 2 cannot go in r7c8 because r7c3 is in this row, r5c8 is in this column, and r9c7 is in this box. Remove the entry or choose a different digit.

4

Naked Triple

Digit 4 cannot go in r7c8 because r6c8 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 4: Naked Triple — Digit 4 cannot go in r7c8 because r6c8 is already in this column. Remove the entry or choose a different digit.

5

Naked Triple

Digit 5 cannot go in r7c8 because r2c8 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 5: Naked Triple — Digit 5 cannot go in r7c8 because r2c8 is already in this column. Remove the entry or choose a different digit.

6

Naked Triple

Digit 6 cannot go in r7c8 because r7c6 is in this row and r9c8 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 6: Naked Triple — Digit 6 cannot go in r7c8 because r7c6 is in this row and r9c8 is in this column. Remove the entry or choose a different digit.

7

Naked Triple

Digit 7 cannot go in r7c8 because r7c5 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 7: Naked Triple — Digit 7 cannot go in r7c8 because r7c5 is already in this row. Remove the entry or choose a different digit.

8

Naked Triple

Digit 8 cannot go in r7c8 because r4c8 is in this column and r8c9 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 8: Naked Triple — Digit 8 cannot go in r7c8 because r4c8 is in this column and r8c9 is in this box. Remove the entry or choose a different digit.

9

Naked Triple

Digit 1 cannot go in r8c8 because r1c8 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 9: Naked Triple — Digit 1 cannot go in r8c8 because r1c8 is already in this column. Remove the entry or choose a different digit.

10

Naked Triple

Digit 2 cannot go in r8c8 because r5c8 is in this column and r9c7 is in this box. Remove the entry or choose a different digit.

Sudoku grid illustrating step 10: Naked Triple — Digit 2 cannot go in r8c8 because r5c8 is in this column and r9c7 is in this box. Remove the entry or choose a different digit.

11

Naked Triple

Digit 4 cannot go in r8c8 because r8c4 is in this row and r6c8 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 11: Naked Triple — Digit 4 cannot go in r8c8 because r8c4 is in this row and r6c8 is in this column. Remove the entry or choose a different digit.

12

Naked Triple

Digit 5 cannot go in r8c8 because r2c8 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 12: Naked Triple — Digit 5 cannot go in r8c8 because r2c8 is already in this column. Remove the entry or choose a different digit.

13

Naked Triple

Digit 6 cannot go in r8c8 because r9c8 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 13: Naked Triple — Digit 6 cannot go in r8c8 because r9c8 is already in this column. Remove the entry or choose a different digit.

14

Naked Triple

Digit 8 cannot go in r8c8 because r8c9 is in this row and r4c8 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 14: Naked Triple — Digit 8 cannot go in r8c8 because r8c9 is in this row and r4c8 is in this column. Remove the entry or choose a different digit.

15

Naked Triple

Digit 9 cannot go in r8c8 because r8c2 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 15: Naked Triple — Digit 9 cannot go in r8c8 because r8c2 is already in this row. Remove the entry or choose a different digit.

16

Naked Triple

Digit 1 cannot go in r9c9 because r9c2 is in this row and r6c9 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 16: Naked Triple — Digit 1 cannot go in r9c9 because r9c2 is in this row and r6c9 is in this column. Remove the entry or choose a different digit.

17

Naked Triple

Digit 2 cannot go in r9c9 because r9c7 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 17: Naked Triple — Digit 2 cannot go in r9c9 because r9c7 is already in this row. Remove the entry or choose a different digit.

18

Naked Triple

Digit 3 cannot go in r9c9 because r5c9 is already in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 18: Naked Triple — Digit 3 cannot go in r9c9 because r5c9 is already in this column. Remove the entry or choose a different digit.

19

Naked Triple

Digit 4 cannot go in r9c9 because r9c3 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 19: Naked Triple — Digit 4 cannot go in r9c9 because r9c3 is already in this row. Remove the entry or choose a different digit.

20

Naked Triple

Digit 5 cannot go in r9c9 because r9c6 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 20: Naked Triple — Digit 5 cannot go in r9c9 because r9c6 is already in this row. Remove the entry or choose a different digit.

21

Naked Triple

Digit 6 cannot go in r9c9 because r9c8 is already in this row. Remove the entry or choose a different digit.

Sudoku grid illustrating step 21: Naked Triple — Digit 6 cannot go in r9c9 because r9c8 is already in this row. Remove the entry or choose a different digit.

22

Naked Triple

Digit 8 cannot go in r9c9 because r9c5 is in this row and r8c9 is in this column. Remove the entry or choose a different digit.

Sudoku grid illustrating step 22: Naked Triple — Digit 8 cannot go in r9c9 because r9c5 is in this row and r8c9 is in this column. Remove the entry or choose a different digit.

23

Naked Triple

These 3 cells contain only candidates 3, 7 and 9 and nothing else.

Sudoku grid illustrating step 23: Naked Triple — These 3 cells contain only candidates 3, 7 and 9 and nothing else.

24

Naked Triple

Because these cells must take the three digits 3, 7 and 9 among themselves, no other cell in the box can keep them.

Sudoku grid illustrating step 24: Naked Triple — Because these cells must take the three digits 3, 7 and 9 among themselves, no other cell in the box can keep them.

25

Naked Triple

These are the other cells in box 9 that still contain 3, 7 and 9 and must be cleaned up.

Sudoku grid illustrating step 25: Naked Triple — These are the other cells in box 9 that still contain 3, 7 and 9 and must be cleaned up.

26

Naked Triple

Remove 3, 7 and 9 from the other cells in box 9.

Sudoku grid illustrating step 26: Naked Triple — Remove 3, 7 and 9 from the other cells in box 9.

27

Result after applying the technique.

Sudoku grid showing the result after applying the technique

Tips & Patterns

Naked Triples don't require all three candidates in each cell.
Look for cells with 2-3 candidates that share digits.
Example: cells with {1,2}, {2,3}, and {1,3} form a Naked Triple.