Lesson 10 of 10 · Subset technique
Hidden triples: three digits with only three homes
The guide and all sudoku lessons
A hidden triple starts with three digits. Within one row, column or box, their possible homes must fit into exactly three empty squares. Those squares have to hold the three digits between them, so any other candidates in those squares can be removed.
You do not need all three digits to appear in every square. One might have two homes and another three. What matters is that their homes, taken together, are the same three squares, with no possible home elsewhere in that unit.
A naked triple clears its digits from other squares. A hidden triple does the reverse: it keeps its three digits and clears other marks from the three squares themselves.
Example 1: In a box
Step 1 of 4
Read every candidate in the middle-left box. Track the possible homes of 1, 2 and 4.
In the middle-left box, every possible home for 1, 2 or 4 is among three squares: row 4, column 2 and row 5, columns 2 and 3. The first square has only 1 and 4; that is still part of the triple.
The 1, 2 and 4 must fill these three squares. At row 5, column 2, that rules out the extra 5. The square is left with 1, 2 and 4, not a single answer.
Example 2: In a column
Step 1 of 4
Read column 9. Where could the 3, 4 and 9 go?
Look for 3, 4 and 9 in column 9. Their only homes are rows 3, 8 and 9. Row 9 does not show a 9, but it is one of the three homes needed by the group.
The ringed square at row 8, column 9 shows 3, 4, 6 and 9. The three reserved digits exclude the 6 there. Its remaining list is still 3, 4 and 9.
Try it yourself
A new board, and the same idea. Get it wrong and the board tells you why.
In the top-middle box, the 1, 5 and 9 can go only in the three marked squares. Which candidate can you remove from the ringed square at row 3, column 6?
Pick one candidate to cross out in the ringed square, not a digit to place.
How to spot it faster
- Choose digits that have only two or three possible homes in a unit, then compare those homes.
- Count the different squares covered by all three digits. The group needs exactly three, not four.
- Read the rest of the unit before removing anything. A single extra home outside the group breaks this restriction.
Common mistakes
Checking only the highlighted squares
The proof is that the three digits have nowhere else in this unit to go. Finding all three among the marks in three squares is not enough.
Erasing the triple's digits
A hidden triple keeps its own digits. The marks to remove are the other candidates inside its three squares.
Questions
Further reading
Try it
Try an expert 9×9 and track digits with few possible homes after the simpler moves run out. Not every expert deal contains a hidden triple, and the free hint still stops at pairs; the worked boards above isolate this technique for practice.
Play solo on an expert 9×9