Techniques › Hidden Quad
Hidden Quad
Four digits confined to four cells. The rarest subset in practical play.
Four digits in a house whose remaining homes span exactly four cells, clearing every other candidate from those cells.
A Hidden Quad is the rarest technique most solvers will ever apply — and that is structural, not luck. In a house with m empty cells, a hidden k-set implies a naked (m−k)-set among the rest, and for a quad the naked form is nearly always the cheaper of the two. Our own engine fires one roughly once in 1,500 puzzles.
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.
| 8 | 9 | 3 | 6 | 5 | 1 | 2 | 7 | 4 |
| 2 | 6 | 7 | 4 | 3 | 9 | 5 | 1 | 8 |
| 1 | 4 | 5 | 2 | 7 | 8 | 3 | 6 | 9 |
| 37 | 12 | 8 | 9 | 46 | 5 | 47 | 23 | 1236 |
| 79 | 5 | 6 | 138 | 2 | 34 | 79 | 348 | 13 |
| 39 | 12 | 4 | 13 | 68 | 7 | 89 | 235 | 12356 |
| 5 | 8 | 9 | 7 | 1 | 234 | 6 | 234 | 23 |
| 6 | 7 | 1 | 35 | 48 | 23 | 48 | 9 | 235 |
| 4 | 3 | 2 | 58 | 9 | 6 | 1 | 58 | 7 |
- NudgeSome digits in box 6 can only go in the same few cells, so nothing else fits there.
- WhereHidden Quad in box 6: r4c7, r5c7, r5c8, r6c7
- Do itRemove r5c8 ≠ 3
How to spot it
Honestly: do not hunt for these. Find them by exhausting everything else in a stubborn house and noticing that four digits have run out of room.
Where you will meet it
Hidden Quad 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 Triple Three digits restricted to the same three cells clear everything else out of them.
- Naked Quad Four cells sharing four candidates between them. Rare, and usually preempted.