Lesson 5 of 7 · Core technique
Hidden singles: the digit with nowhere else to go
The guide and all sudoku lessons
A naked single is a square with one candidate. A hidden single turns that around: a digit with one possible square. Look at a row, a column or a box and ask, for one digit, where it could go. If only one empty square can take it, the digit goes there, however many other candidates that square has.
It is called hidden because the square itself does not give it away. Its marks might read 1, 4 and 7, and nothing about the square alone says 7. The answer only shows when you look across the whole unit and see that the 7 has no other home.
Scanning finds hidden singles by eye. With pencil marks on the board, you can read them off instead: a digit marked in exactly one square of a unit.
Example 1: In a box
Step 1 of 5
Ask where a digit can live: where can the 3 go in the centre box?
Read the marks across the centre box. None of its eight empty squares is down to one candidate, so there is no naked single to take. But look at the 3: it appears in only one square, row 4, column 6, which could also be a 1, a 4 or an 8. The 3 has to go somewhere in this box, and that square is the only place it can.
Example 2: In a column
Step 1 of 4
Where can the 7 go in column 6? It has five empty squares.
Hidden singles hide in rows and columns too. Column 6 has five empty squares. Write their marks, and the 7 appears in only one of them: row 7, which could also be a 1 or a 4.
Each of the other four is ruled out by a 7 it can see. Rows 2, 4 and 8 each already hold a 7, and the square in row 6 shares a box with the 7 in row 4. With nowhere else to go in the column, the 7 goes in row 7.
Try it yourself
A new board, and the same idea. Get it wrong and the board tells you why.
Where must the 3 go in the highlighted row? Tap the square.
Tap a square on the board.
How to spot it faster
- Go digit by digit. For each digit, check each box, then each row and column, for a unit where it has a single possible square.
- With marks on, scan a unit for a digit that appears exactly once. That is faster than checking squares one by one.
- Look first at digits that already appear many times on the board: they have the fewest homes left.
- After a placement, look again at its row, column and box. The square you filled was a possible home for other digits too, and one of them may now have only one square left.
Common mistakes
Looking only at the square
A hidden single never shows in the square itself; it may have three or four candidates. You find it by looking at the unit for one digit.
Checking one unit and stopping
A digit can have several homes in its row and one home in its box. The box is what decides it; the row tells you nothing either way.
Reading stale marks
If a mark should have been removed and was not, a digit can look like it has two homes when it has one, or one when it has none. Keep marks up to date before trusting them.
Questions
Try it
On a medium board with marks on, pick a box and read across it for a digit marked only once. Then try the same along a row and a column.
Play solo on a medium 9×9