Hidden singles

What it is

A hidden single is a digit that has only one possible home in a row, a column or a box. The cell itself may still have several candidates written in it, which is why the single is “hidden”. But because the digit has nowhere else to go in that row, column or box, it must go in that cell.

The difference from a naked single is the question you ask:

• A naked single asks: “which digits can go in this cell?” and finds only one.
• A hidden single asks: “where can this digit go in this row, column or box?” and finds only one cell.

Cross-hatching, from our scanning guide, is simply a way of finding hidden singles in boxes.

How to spot it

Pick a row, column or box with a few empty cells. For each digit it is missing, check every empty cell and ask whether that digit could go there. If all but one cell is blocked, you have a hidden single.

If you keep full pencil marks, look for a digit that appears in the notes of only one cell within a row, column or box. That cell is a hidden single, whatever else is noted in it.

A worked example

Look at row 6, which is missing several digits. Its empty cells are in columns 2, 4, 5 and 8. Let us find where the 3 goes.

• Column 2 already has a 3, up in row 1. So row 6, column 2 cannot be 3.
• Columns 4 and 5 of row 6 are both in box 5. Box 5 already has a 3, at row 4, column 6. So neither row 6, column 4 nor row 6, column 5 can be 3.
• Row 6, column 8 is in column 8 and box 6, and neither of those has a 3 yet.

So the only cell in row 6 that can hold the 3 is row 6, column 8. The 3 goes there.

Now suppose your notes for row 6, column 8 said 3, 5 and 6. If you only looked at that cell, you would see three options and move on. The hidden single only shows up when you look at the whole row and ask where the 3 can go.

Which units to check

Boxes are the most natural place to look, because you can cross-hatch them by eye. But rows and columns hide singles too, and they are easier to miss. When boxes run dry, sweep each row and column with one question in mind: “is there a digit here with only one place left?”

A common mistake

The classic mistake is mixing up the two kinds of single. A player sees three notes in a cell, decides “nothing to do here”, and moves on. Always check the other direction: even if a cell has several candidates, one of them might be the only option for its row, column or box.

The other mistake is forgetting a filled cell’s effect on a whole box. In the example, it was the 3 in box 5 that blocked two cells of row 6 at once. Look at the boxes a row passes through, not just the columns.

When you will need it

Hidden singles, together with naked singles, are all you need for an Easy puzzle on sudoku.ie. They are just as important on harder days: after a clever elimination from pointing or an X-wing, the next placement is very often a hidden single.