Hidden Single

There is a hidden single when, in a unit (a row, a column or a box), there is only one cell where a number can go. Since the number has to appear in the unit, it belongs in that cell, even if the cell has other candidates.

It is called hidden because the cell, seen on its own, doesn't give it away: it may have three or four candidates. What reveals it is looking at the whole unit and seeing that every other cell is already ruled out for that number, which is exactly what scanning does.

Not only in boxes

In the scanning article we searched inside a box. The same question works in a row or a column. Some hidden singles can only be seen that way.

1. Row 1 is missing four numbers: the 2, 3, 4 and 6. Where can the 2 go?
2. Column 5 already has a 2, in row 6. The cell of row 1 in that column is ruled out.
3. Box 3, in the top right corner, also already has its 2, in row 2. The two empty cells of row 1 in that box are ruled out.
4. The first cell of the row is left: the 2 goes there, even though that cell also has the 4 and the 6 as candidates. Scanning box 1 or column 1 would not show it: in those units the 2 still has more than one place.

Hidden single and naked single

There is another way for a number to claim a cell: the cell can only hold that number. That is a naked single, which you see the other way round: instead of looking for the cell where a number goes, you look for the number missing from a cell. The hidden single can be seen without writing anything; the naked single almost always needs pencil marks.

How to search

• In each box, go through the numbers it is missing and see whether any has only one place.
• Do the same in rows and columns with few empty cells: with three or four gaps, the options run out quickly.
• In an Easy puzzle almost everything is solved with hidden singles. When you get stuck, it is often because one was in plain sight.

Your turn

Find a hidden single and place the number. There is almost always more than one. Any of them will do.