Naked and Hidden Singles: Two Ways to Prove One Digit

Count digits or count locations

The word single describes a forced placement, but you can reach it from two directions. A naked single has only one remaining candidate in its cell. A hidden single is the only location for a particular digit in a row, column or box. HoDoKu distinguishes these definitions explicitly. [1]

Keep the question visible while searching. For a naked single, choose a cell and cross off digits. For a hidden single, choose a missing digit and cross off cells. Confusing the two is not disastrous if the proof is correct, but it can make you repeat the same unsuccessful scan without noticing another kind of evidence.

One cell, one surviving candidate

The first row diagram contains every digit except 5. Its fifth cell has candidate set {5}; placing 5 completes the row. This nearly completed house is a particularly simple single. A naked single can also be created by combining information from several houses rather than finding eight answers in one row.

For example, a target cell's peers might collectively contain 1, 2, 3, 4, 6, 7, 8 and 9, spread across its row, column and box. Their positions do not need to form a pattern. What matters is that they exclude all eight alternatives. Before placing 5, check that each exclusion is based on a confirmed digit or a sound earlier deduction.

One digit, one remaining address

Now inspect the second diagram by digit. The unresolved cells have lists {2,5}, {2,6}, {5,6,9} and {2,6}. Look for 9. Only column 5 contains it, so that row's 9 must go there. The extra 5 and 6 notes in that cell do not prevent the placement; the row's requirement for a 9 overrides them.

This is the digit-first view illustrated in Stuart's introductory guide. [2] Our row model has two compatible arrangements for the other unresolved digits, but both put 9 in c5. You have proved one answer without needing to settle the entire row.

After placing 9, inspect digit 5 again. It now survives only in c2. The first hidden single exposes another. You can follow that consequence while leaving the two remaining {2,6} cells unresolved.

One written mark is not always one possibility

These examples assume the candidate information needed for the proof is complete. If you have marked only the positions for 9, an isolated 9 note says nothing about whether the cell also allows 2 or 6. Similarly, finding one visible 9 in a partially annotated row does not prove that other cells cannot contain it.

Check unfilled, unannotated cells before making the placement. A candidate list is evidence only to the extent that you know how it was constructed. The pencil-marks guide explains that distinction in detail.

Also avoid reading a candidate as a placed digit. A large confirmed 6 excludes 6 from its peers. A small 6 note does not: it is one of the unresolved choices you are still comparing.

Return to the cells that changed

After a placement, remove its digit from the affected row, column and box. Conceptis includes these three kinds of restriction in its single-candidate examples. [3] Then inspect the changed lists before searching elsewhere.

Use the hidden-single row above as a rehearsal. Place 9 in c5, find 5 only in c2, and stop at the remaining {2,6} pair. The correct stopping point matters. A sequence of successful moves can tempt you to keep filling cells after the evidence has run out. Here, nothing in the row alone chooses the pair's order.

On a full board, the pair's columns or boxes may provide the next restriction. That is a new proof, not a continuation you are allowed to assume.

A stalled scan is information, not failure

If every unresolved cell has several candidates and every missing digit has several locations in each house, these two tests produce no move. Repeating them without new information will not manufacture a single.

First check that your notes are accurate. Then inspect a different relationship, such as a box-line interaction or a naked pair. An elimination may create a fresh single, sending you back to the same simple questions. This is why singles remain useful after learning more elaborate patterns.

Try the quiz by naming whether each proof counts digits or counts locations. That short distinction is more useful than memorising which name sounds easier.