Hidden singles: only one possible place
Switch from asking what fits in this cell to asking where this digit can go.
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A hidden single may sit in a cell with several candidates. Yet inside its row, column or box, one particular digit has no other legal position.
Scan one digit
Choose a digit that already appears often. Inspect each box and use matching digits in neighboring rows and columns to eliminate positions.
- Follow one digit at a time
- Start within boxes
- Confirm with candidates
The common blind spot
Several candidates in a cell do not mean you must wait. Zoom out and check whether one of those digits has anywhere else to go in the region.
Worked example: one position for a digit
Suppose a row has three empty cells, A, B and C, with complete candidate sets A={2, 6}, B={2, 6, 8}, C={2, 6}. The digit 8 is missing from the row and appears only in B. Therefore B must be 8, even though B has three candidates.
A naked single has one candidate in one cell. A hidden single has one possible cell for one digit within a region. Here none of the three cells is initially a naked single, but the row still gives a certain move.
Check every empty position
Exercise: A={1, 4}, B={1, 4, 7}, C={4, 7}. Is 7 a hidden single? No: it can go in B or C. Having fewer possible positions is not enough; there must be exactly one.
Check the whole row, column or box, including cells where you have not written notes. A missing candidate note can make a number seem unique when it is not. After a confirmed placement, scan the intersecting regions again.