Most beginners look for a cell with one candidate left, a naked single. A hidden single flips that question around. Instead of asking what a cell can hold, you ask where a digit can go. Pick a row, column or box, pick a digit that is missing from it, and check every blank cell in that unit. If only one of them can legally take that digit, it has to go there, no matter how many other candidates that cell also has.
The name comes from pencil marks. If you wrote out full candidate lists for a row, the digit might appear in only one list out of five or six, buried among two or three other digits. It is "hidden" there rather than sitting alone the way a naked single does. Once you notice it, the placement is exactly as certain as a naked single. Nothing is guessed.
Hidden singles turn up constantly on this site's puzzles. Easy boards (40 or more givens) can be finished with hidden and naked singles alone. Medium boards (33 to 39 givens) lean on hidden singles even more, since cells often keep three or four live candidates for a while before one digit gets forced out by its row, column or box.
Worked example
A real puzzle. Row 5 has five open cells; step through their candidates to see why 6 can only go in one of them.
Finding a hidden single from candidate lists
Write out (or picture) the candidates for every blank cell in one row, column or box. Then go digit by digit, from 1 to 9, and count how many of those lists contain each one. Most digits will show up in two, three or more cells. The moment you find a digit that shows up in exactly one list, you have a hidden single, regardless of how long that cell's own list is.
This is easiest inside a box, since a box has the fewest cells to scan through at once, but the same counting works across a full row or column too.
Hidden single or naked single?
A naked single is found by looking at one cell: does it have exactly one candidate? A hidden single is found by looking at one digit across a whole unit: does it have exactly one legal cell? A cell can be a hidden single while still showing three or four candidates on the page, because the other candidates simply never had anywhere else to go for that digit specifically.
In practice the two overlap constantly. Scanning is the fast, eyes-only way most players find hidden singles in a box without writing anything down. Full candidate lists, the approach used here, catch hidden singles in rows and columns just as reliably, and they catch ones that scanning alone tends to miss.
Common mistakes
- Assuming a busy cell cannot be a single. A cell with four pencil marks looks unfinished, but if one of those four digits has no other home in the row, column or box, it is still forced. Do not skip cells just because their own candidate count is high.
- Checking only the box. Hidden singles happen in rows and columns just as often as boxes. If you only ever scan boxes, you will miss the ones sitting in a mostly-empty row or column.
- Working from stale notes. If you filled in a cell and did not clear that digit from the pencil marks of its peers, a real hidden single can hide behind an extra candidate that should no longer be there. On this site, placing a digit clears it from every peer's notes automatically.
Why hidden singles matter
Naked singles only appear once a cell has been whittled all the way down to one option, which usually means the board is already crowded. Hidden singles appear earlier, as soon as a digit runs out of room in a unit, even while individual cells still look wide open. That makes them the technique that keeps a puzzle moving in its early stages, before naked singles have much to work with.
Turn on the Notes button in the game to see every candidate at once, or use the Hint button (three per puzzle) if a hidden single is proving hard to spot; it will place one for you at the cost of some score.
Turn on Notes and watch a digit disappear from every candidate list but one. That cell is a hidden single.
Frequently asked questions
A hidden single is a digit that has only one possible cell left within a row, column or box, even though that cell may still show other candidates. The digit is placed because it has nowhere else to go.
A naked single is a cell with exactly one candidate. A hidden single is a digit with exactly one legal cell in a unit, and that cell can still list several other candidates.
Not necessarily. Scanning, tracing the rows and columns a digit already occupies, finds most hidden singles in a box without writing anything down. Full pencil marks make hidden singles in rows and columns easier to catch.
Boxes, since they only hold nine cells and often already have several digits placed. Rows and columns also produce hidden singles, especially once a box has been mostly filled in.
Easy puzzles on this site are generated so naked and hidden singles together are always enough to finish. Medium boards rely on them for most placements before harder moves are needed.
Those extra candidates were never eliminated locally; they only became irrelevant once you checked the wider row, column or box and found the digit had no other home. The cell itself was not down to one option, the digit was down to one cell.