The digit that has only one home left

The short version

A hidden single is a digit with exactly one legal cell inside a unit — one row, one column, or one box. That cell must take the digit, even if it still has other candidates.

The trap is in the name. Every other cell in the unit has already been ruled out for this digit, by something already on the board. The cell that survives does not look special. It is usually the last place you look.

How it hides

Take a digit and a box. Walk the nine cells. Six of them already contain numbers, so they are irrelevant. Of the three empty cells, two are blocked because the digit already appears in their row or column.

One cell remains. That is a hidden single.

Now look at that cell's own candidate list. It might read {2, 5, 8}. Nothing about those three candidates tells you the cell is solved. The information is not in the cell — it is in the absence of anywhere else to put the 5.

This asymmetry is why beginners miss it constantly. A naked single shouts: one candidate, fill it. A hidden single is silent, and you only hear it if you are counting a specific digit.

A real board

The claim is narrow and checkable: inside the top-middle box, 5 has exactly one home, R2C6.

• The box has three empty cells: R2C4, R2C5, R2C6.
• R2C4 is out because there is already a 5 in column 4.
• R2C5 is out because there is already a 5 in column 5.
• R2C6 is the only cell in the box that can still hold a 5.

So R2C6 is 5 — regardless of what else that cell could have been. The other candidates in R2C6 were never consulted.

How to scan for one

Scan by digit, not by cell. This is the habit that separates people who find hidden singles from people who stare at the board.

1. Pick a digit, start with boxes. Boxes are the smallest unit and the most constrained, so hidden singles surface there first. For digit 5, check each box: how many empty cells can still take a 5?
2. Count, do not solve. You are not evaluating candidates. You are asking "where can this digit still go?" — a much cheaper question.
3. Move to rows, then columns. A digit that is blocked in every box may still be hidden in a row. Rows and columns each have nine cells, so they take longer, but they catch what the boxes miss.
4. Advance the digit. Do not switch digits while you still have unanswered boxes. Finish 1 through 9, then restart, because each placement you make changes the answers for the next pass.
5. Restart the sweep. Every number you write down can create a new hidden single two digits later. The sweep is not a single pass; it is a loop.

A practical ordering that works well: boxes first with all nine digits, then rows and columns only for the digits that are still unresolved. Most puzzles fall apart within two sweeps.

Hidden single vs naked single

They are mirror images, and the difference is direction:

• A naked single is found from the cell: one cell, one surviving candidate.
• A hidden single is found from the digit: one digit, one surviving cell.

Both produce a forced placement, and the same cell can satisfy both descriptions at once. When that happens, you have found the same move twice, which is a good sign rather than a redundancy.

The practical difference is cost. Naked singles require you to know every cell's full candidate list. Hidden singles require you to look at one digit at a time. That makes hidden singles cheaper, and on easier puzzles you will finish without ever writing a candidate down.

The trap: one home, not one candidate

The single most common error is treating "the digit can only go here in this box" as if it also meant "this cell can only be this digit". It does not. The cell might have three candidates and you are only entitled to conclude one thing: the digit goes there.

A second trap is scanning only boxes. Boxes are where hidden singles are easiest to spot, so solvers stop there. But a digit can be exhausted in every box and still be a hidden single in a row, because a row spans three boxes and the eliminations that matter may come from far outside the box you were staring at.

There is a third, quieter trap: the digit must have exactly one home. If you find two cells in a box that can both take the digit, you have found nothing — that is a two-home situation, and it is the raw material for pairs and X-Wings, not a placement.

Where to use it

Hidden singles are the workhorse of every easy and medium puzzle, and they never stop being useful. Even on advanced boards, the move that finally cracks the puzzle is often a hidden single that appeared three eliminations ago.

They are also the first technique worth practising deliberately. Set a timer, take one digit, sweep every box and row, and count how long it takes to exhaust it. The skill transfers directly: the same sweep is the first step of scanning a hard board.