Techniques › Hidden Triple
Hidden Triple
Three digits restricted to the same three cells clear everything else out of them.
Three digits in a house whose remaining positions fall within the same three cells. Those cells must take those digits, so any other candidates in them go.
Hidden Triples are genuinely hard to spot and, in practice, rarer than their difficulty suggests — a house with a Hidden Triple usually also contains a simpler deduction. They are worth learning mostly for the pattern-recognition they build.
A worked example
Taken from a real puzzle in our bank, at the point where this was the cheapest move available. Pattern candidates are marked in amber; anything the step eliminates is struck through in red.
| 156 | 167 | 25 | 57 | 4 | 26 | 3 | 8 | 9 |
| 9 | 367 | 23 | 37 | 8 | 26 | 4 | 5 | 1 |
| 58 | 38 | 4 | 35 | 9 | 1 | 6 | 7 | 2 |
| 15 | 13 | 35 | 2 | 7 | 9 | 8 | 6 | 4 |
| 46 | 46 | 8 | 1 | 3 | 5 | 9 | 2 | 7 |
| 2 | 9 | 7 | 8 | 6 | 4 | 5 | 1 | 3 |
| 3 | 2 | 9 | 6 | 1 | 8 | 7 | 4 | 5 |
| 7 | 5 | 6 | 4 | 2 | 3 | 1 | 9 | 8 |
| 48 | 48 | 1 | 9 | 5 | 7 | 2 | 3 | 6 |
- NudgeSome digits in box 1 can only go in the same few cells, so nothing else fits there.
- WhereHidden Triple in box 1: r1c1, r1c2, r2c2
- Do itRemove r1c1 ≠ 5, r2c2 ≠ 3
How to spot it
Within one house, list the homes of each unplaced digit. Look for three digits whose homes together span only three cells.
Where you will meet it
Hidden Triple sits at tier 2 of our ladder, which means it first becomes necessary at Medium. Puzzles below that band never require it, though it may still appear as a shortcut.
Read next
- Hidden Pair Two digits that can only go in the same two cells own them, whatever else those cells show.
- Naked Triple Three cells sharing three candidates between them lock those digits away.
- Hidden Quad Four digits confined to four cells. The rarest subset in practical play.