Lesson 9 of 10 · Subset technique
Naked triples: three squares, three digits
The guide and all sudoku lessons
Look for three empty squares in one row, column or box whose candidates add up to just three different digits. Those squares must take those three digits between them. No other square in that unit can use any of them.
The three squares do not have to show identical marks. Lists such as 2 and 3, 2 and 8, and 3 and 8 still use only three digits in total: 2, 3 and 8. Each list is part of the same triple.
Like a naked pair, a triple removes candidates outside its own squares. It does not tell you which of the three digits goes in each square.
Example 1: In a row
Step 1 of 4
Read the candidates across row 4. Look for three squares that together use only three digits.
In row 4, columns 4, 7 and 9 show only 4, 5 and 6 between them. The first two squares each show all three digits; the third shows just 4 and 6.
These three squares need three different values, and have only those three digits to choose from. That uses every 4, 5 and 6 in row 4. The ringed square at column 3 shows 2, 4 and 7, so its 4 can go. It is still undecided between 2 and 7.
Example 2: Three different pairs in a box
Step 1 of 4
Read the empty squares in the top-middle box. This triple will not look like three identical lists.
The top-middle box contains a less obvious triple. Row 1, column 4 shows 2 and 3; row 2, column 5 shows 2 and 8; row 3, column 4 shows 3 and 8.
No two squares have the same pair. Taken together, though, they have just three possible digits: 2, 3 and 8. That leaves no room for a 2 at row 1, column 5, whose other candidates are 5 and 9.
Try it yourself
A new board, and the same idea. Get it wrong and the board tells you why.
In row 2, columns 2, 3 and 8 form a triple using 4, 7 and 8. Which candidate can you remove from the ringed square at row 2, column 7?
Pick one candidate to cross out in the ringed square, not a digit to place.
How to spot it faster
- Start with squares showing two or three candidates. Combine their lists; count different digits, not the total number of marks.
- Try three related lists such as 2/3, 2/8 and 3/8. A triple can be built entirely from two-candidate squares.
- Before clearing a mark, check that the target square is outside the triple but inside the same row, column or box.
Common mistakes
Demanding three identical lists
That is one form of a naked triple, not the rule. What matters is that the three squares have only three different candidates between them.
Clearing a digit inside the triple
The triple's squares still need their candidates. Its effect is on other squares in the shared unit.
Questions
Further reading
Try it
Try an expert 9×9 and compare small candidate lists once the simpler moves run out. Expert boards need reasoning beyond pairs, but a particular deal may need a different technique rather than a naked triple.
Play solo on an expert 9×9