Hidden singles: the first Sudoku technique to learn
A hidden single is a number that can only go in one square of a row, column or box. You place it there even when that square could hold other numbers, which is why it is called hidden.
It is the move that solves our Easy Sudoku puzzles, and once you can spot it quickly, most of Medium opens up too. Below are two worked examples from a real Easy puzzle, then the habits that make the move automatic.
What does a hidden single look like on a real grid?
This puzzle came out of our Easy level and starts with 41 numbers. Rows are numbered from the top and columns from the left.
Take the bottom left box. It has seven empty squares and no 3 yet. Where can the 3 go?
- Row 7 already has a 3, in column 7. That rules out the two empty squares of the box in row 7.
- Row 9 has a 3 in column 4. That rules out all three squares of the box in row 9.
- Column 3 has a 3 in row 1. That rules out the square in row 8, column 3.
Six of the seven squares are ruled out, so the 3 goes in row 8, column 1.
Why is it called a hidden single?
Look at row 8, column 1 on its own and it could be a 2, 3, 5, 8 or 9. Nothing about the square says 3. The answer only shows when you turn the question around and ask where the 3 can go in the box, instead of what can go in the square.
The other kind of single works the first way. A naked single is a square where only one number fits, because the other eight are already in its row, column or box. Both are worth knowing, but hidden singles are easier to find by eye, because you follow one number at a time instead of eight. Our Sudoku strategy guide covers both, and the pairs that come after them.
Do you only check boxes?
No. A row or a column also needs every number once, so the same idea works there. Sometimes a box gives you nothing and the row through it does.
With the 3 in place, look at row 1. It is missing 2, 7, 8 and 9, and its empty squares are in columns 2, 7, 8 and 9. Where can the 2 go?
- Column 2 has a 2 in row 3.
- Column 7 has a 2 in row 6.
- Column 8 has a 2 in row 7.
That leaves column 9, so row 1, column 9 is a 2. If you had scanned the top right box for a 2 instead, you would have found two possible squares, rows 1 and 2 of column 9, and moved on. The row settles it.
How do you spot hidden singles faster in the game?
The game does a lot of the looking for you:
- Tap a number on the board. Tap any 3 and every 3 lights up. The rows and columns that already have a 3 stand out, so the squares they rule out are easy to see.
- Tap an empty square. Its row, column and box are shaded, so you can check one square against all three before you place anything.
- Read the number pad. The small number on each key shows how many of that number are still to place. A key with 1 or 2 left is a good one to scan first, because most of its rows and columns are already taken. The key fades once all nine are placed.
- Leave Notes OFF. Hidden singles on Easy need no notes. Our post on when to use pencil marks explains when they start to pay off.
The Mistakes counter shows 0 / 3, and a third mistake ends the game. That is a good reason to be sure before you place, and a hidden single gives you that: once every other square is ruled out, the number has nowhere else to go.
Can you finish an Easy puzzle with hidden singles alone?
Yes. We made 1,000 puzzles with the same generator our Easy level uses and had a computer solve each one using nothing but hidden singles. All 1,000 were finished that way.
Some more numbers from the same test:
- Every puzzle started with 41 or 42 numbers.
- 992 of the 1,000 could be finished by scanning boxes alone, without ever checking a whole row or column.
- Every puzzle had at least three squares you could fill by scanning boxes at the very start, and about 12 on average.
- Naked singles alone finished 982 of the 1,000. That is close, but hidden singles never ran out, which is why we suggest learning them first.
So if you are stuck on Easy, a hidden single is waiting somewhere on the board. Go through the numbers 1 to 9 again and one will turn up. Press Hint only if a full sweep finds nothing.
Can you find the next one?
Stay on the same grid. Column 7 has five empty squares, in rows 1, 2, 3, 5 and 8, and no 6. The pad would show only two 6s left to place, so it is a good number to try. Where does the 6 go?
Show the answer
Row 2. Rows 1, 3, 5 and 8 each already have a 6, so only row 2, column 7 is left, even though that square could also be a 4 or a 5.
What else do people ask about hidden singles?
Do I need notes to find hidden singles?
No, not on Easy. You can find every hidden single by looking along rows, columns and boxes. Notes start to help on Hard and above, when a number has two or three possible squares and you want to keep track of them.
Are hidden singles enough for Medium Sudoku?
Almost always. In our test of 1,000 Medium puzzles, 983 could be finished with hidden singles alone. The other 17 needed a naked single or a harder step.
What should I learn after hidden singles?
Naked singles, then naked pairs. Both are in our strategy guide, in the order you will need them.
Which habits should you practise?
- Ask where a number goes, not what a square holds. That one switch is the whole technique.
- Go number by number. Pick one number and check every box that is missing it before you move to the next.
- Start with the fewest left on the pad. Fewer to place means fewer squares to check.
- Tap a number to light up every copy. Let the highlights rule squares out for you.
- Check the row and column, not just the box. When a box gives you two squares, the row or column through them often settles it.
- Rule out every other square before you place. That keeps Mistakes at 0.
Play Easy Sudoku now and look for your first hidden single on a fresh puzzle.
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