Hidden Triples

Volodymyr Sakhan  ·  May 9, 2026

A hidden triple is one of the most satisfying patterns to spot in sudoku. Once you find it, you can eliminate several candidates at once and often place a digit immediately. Like Hidden Pairs, the pattern is called "hidden" because the key digits are buried among extra candidates in each cell.

This article walks through what a Hidden Triple is, when to look for one, and how to apply it in a row, a column, and a box — with three fully worked examples.

What Is a Hidden Triple?

A Hidden Triple occurs when exactly three digits appear as candidates in only three cells of a house (row, column, or box) — and nowhere else in that house. Because each of those three digits must be placed in one of the three cells, any other candidates those cells contain are impossible and can be eliminated.

Compare this with a Naked Triple: in a Naked Triple, three cells hold only the three candidate digits between them (no extras). In a Hidden Triple, the same three cells also carry additional candidates — that is what makes the triple hard to see. The logical conclusion is identical: those three cells are reserved for those three digits.

When to Use Hidden Triples

Look for Hidden Triples when you have stalled on simpler techniques and your grid has full pencil marks. They appear most often at medium difficulty and above. Three signs suggest the right moment:

• Naked Singles, Hidden Singles, and Naked/Hidden Pairs are all exhausted.
• A house has several cells still unsolved and candidate counts feel crowded.
• Scanning digit-by-digit reveals two or three digits each limited to the same small group of cells.

Step-by-Step Examples

Each example below shows a different type of house. The triple digits are highlighted in green inside the pattern cells; extra candidates to be eliminated are shown in plain grey.

Hidden Triple in a Row

In this puzzle, row 9 has several unsolved cells. Scanning which digits can go where reveals a Hidden Triple {4, 5, 7} in cells B9, D9, and I9.

1. Write complete pencil marks for every empty cell in row 9.
2. For each digit 1–9, count how many cells in row 9 can hold it.
3. Digit 4 appears in only two cells of row 9: B9 and D9.
4. Digit 5 appears in only two cells: D9 and I9.
5. Digit 7 appears in only two cells: D9 and I9.
6. Together, digits {4, 5, 7} appear collectively in only three cells: B9, D9, I9. Those three cells must hold exactly one of {4, 5, 7} each.
7. Eliminate all non-triple candidates: remove {1, 3, 6} from B9 → B9 = {4}; remove {6} from D9 → D9 = {4, 5, 7}; remove {1, 3} from I9 → I9 = {5, 7}.
8. B9 is now solved: digit 4 is placed in B9 immediately.

When three digits appear exclusively in three cells of a row, those cells form a Hidden Triple — every other candidate in those three cells can be cleared.

Hidden Triple in a Column

Here column I has several unsolved cells. A digit-by-digit scan reveals the Hidden Triple {2, 3, 7} locked to cells I4, I7, and I9.

1. Write complete pencil marks for every empty cell in column I.
2. For each digit 1–9, identify which cells of column I can hold it.
3. Digit 2 appears in only two cells of column I: I4 and I7.
4. Digit 3 appears in only two cells: I4 and I7.
5. Digit 7 appears in only two cells: I7 and I9.
6. Together, digits {2, 3, 7} appear collectively in only three cells: I4, I7, I9. Those three cells must hold exactly one of {2, 3, 7} each.
7. Eliminate all non-triple candidates: remove {6} from I4 → I4 = {2, 3}; remove {6, 9} from I9 → I9 = {7}.
8. I9 is now solved: digit 7 is placed in I9 immediately.

When three digits are confined to three cells of a column, any extra candidates in those cells can be removed — and if a cell ends up with only one digit, it is solved.

Hidden Triple in a Box

In this puzzle, box 3 (top-right, columns G–I, rows 1–3) contains three cells that form a Hidden Triple. Digits {1, 2, 6} appear in box 3 only in cells G1, G2, and H2.

1. Write complete pencil marks for every empty cell in box 3.
2. For each digit 1–9, check which cells of box 3 can hold it.
3. Digit 1 appears in only two cells of box 3: G2 and H2.
4. Digit 2 appears in only three cells of box 3: G1, G2, and H2.
5. Digit 6 appears in only two cells of box 3: G2 and H2.
6. Together, digits {1, 2, 6} appear collectively in only three cells: G1, G2, H2. Those three cells must hold exactly one of {1, 2, 6} each.
7. Eliminate all non-triple candidates: remove {3, 8} from G1 → G1 = {2}; remove {3, 8} from G2 → G2 = {1, 6}; remove {8} from H2 → H2 = {1, 2, 6}.
8. G1 is now solved: digit 2 is placed in G1 immediately. After that, 2 is also removed from H2, leaving H2 = {1, 6}.

When three digits are confined to three cells of a box, the triple is hidden among extra candidates — eliminating the extras reveals locked cells and often solves one immediately.

Hidden Triples and Related Techniques

Hidden Triples belong to the same family as Hidden Pairs and Hidden Quads. Understanding how they relate helps you scan more efficiently:

• Naked Triples and Hidden Triples are complementary: every Hidden Triple in a house implies a Naked Triple in the remaining cells, and vice versa. If one scan fails, try the other perspective.
• Hidden Pairs are more common than Hidden Triples. Always check for pairs first before looking for triples — they are faster to spot and easier to verify.
• Hidden Quads are rarer still and much harder to find by hand. In practice, if three digits share three cells, spotting the triple is more practical than searching for the complementary quad.
• There are no hidden quintuples: five hidden candidates would imply a complementary quad in the remaining four cells — always the easier pattern to find.

Practical tip: scan each digit's positions in a house one at a time. When you notice two or three digits that share the same two or three cells, you have found a hidden set.

Practice Hidden Triples Online

The best way to get comfortable with Hidden Triples is to play puzzles at the right difficulty level. Medium sudoku regularly features this pattern, and our solver shows pencil marks automatically so you can focus on spotting the triple.

You can also review our full solving guide for a complete progression from beginner to advanced techniques.

Frequently Asked Questions