What is a hidden triple?
A hidden triple is a pattern in a single house (a row, column or 3x3 box) where exactly three digits can only appear in exactly three cells of that house. The three digits are "hidden" because each of those three cells may also contain other candidates. Once you identify a hidden triple, you can remove every other candidate from those three cells — because the three digits must occupy those three cells in some order.
How a hidden triple differs from a naked triple
A naked triple is when three cells contain exactly the same three candidates (or subsets that together cover three numbers) and nothing else; the triple is visible directly in the candidate lists. A hidden triple is the opposite: the three digits appear only in those three cells, but the cells may list extra candidates. In practice you often use both ideas in the same solve: spotting a hidden triple can convert the three cells into a naked triple by eliminating the extra candidates.
When to look for a hidden triple
- After you have placed obvious singles and eliminated easy candidates. Hidden triples are a mid-level technique — not the first thing to try, but useful before moving to much harder methods.
- Check each house after candidates have been updated from simpler steps (singles, pairs, box/line interactions, and naked triples). Hidden triples often appear once the obvious eliminations have been made.
- They are especially helpful when many cells in a house remain unsettled and no single or pair progress is available.
Step-by-step detection
1) Pick a house to inspect (a row, column or box).
2) Build a map of which candidates appear in which cells of that house. For each digit 1–9, list the cell positions in the house where that digit can still go.
3) Look for three digits whose possible positions are a combined set of exactly three distinct cells. That is, the union of the cell lists for those three digits has size three.
4) Confirm no other cell in the house is listed for any of those three digits. If the union contains exactly three cells, you have a hidden triple.
5) Eliminate all other candidates from those three cells. After elimination they become a naked triple, meaning no other values can appear in those three cells.
Example and what to eliminate
Below you will find a candidate-grid visual showing a hidden triple in a single row. In the example, digits 2, 5 and 7 are the only cells in that row that can take those digits, and those three digits are confined to exactly three cells. The three cells also contain other candidates, so the triple is hidden. Once found, remove the non-2/5/7 candidates from those three cells.
How to use the example in practice
- Confirm the pattern by checking all other cells in the same row: none of them should list 2, 5 or 7 as a candidate.
- Clear every other candidate from the three focus cells — that gives you three cells that contain only {2,5,7}.
- After that elimination, use the usual follow-up logic: maybe one of those three cells becomes a single, or that naked triple allows further eliminations in overlapping houses.
Common mistakes to avoid
- Don’t assume three cells that each contain one of the digits automatically form a hidden triple. The key is that the three digits appear only in those three cells and nowhere else in the house.
- Don’t mix houses: the triple must be contained within a single row, column or box.
- Be careful when reading candidates: pencilmarks must be up to date. Hidden triples typically appear after several eliminations — working with stale candidates leads to false patterns.
Practice tips
- Scan houses by looking at low-frequency candidates first. Digits that appear in only two or three cells are good starting points to spot hidden triples.
- Keep your candidate lists neat: it’s easier to compare digit positions across a house when marks are ordered.
- Use hidden triples as a follow-up when easier methods stall. They often unlock a next step rather than solve the house outright.
Summary
Hidden triples are a compact, powerful tool: three digits hidden in three cells let you eliminate other candidates from those cells and often create a cascade of easier moves. With careful candidate maintenance and a habit of scanning houses for digits confined to few cells, you’ll spot hidden triples reliably and gain a useful way to progress medium-difficulty puzzles.