Naked Singles and Hidden Singles
Singles are the bread and butter of Sudoku. Every Easy puzzle can be solved with nothing else, and even Master puzzles spend most of their time on singles.
Hidden singles: "only one place for this number"
A hidden single happens when a number can go in only one cell of a box, row or column. The cell might have other candidates too, which is why it is "hidden", but because every unit must contain each number once, that number has to go there.
To find one, pick a number and a box. For each empty cell in the box, ask: is this number already in the cell's row or column? Cross off every cell that is blocked. If exactly one cell survives, you have found a hidden single.
Unit being checkedBlocking numberTarget cell
In the example, we are looking for the 5 in the top-left box. The 5 in the second row blocks every empty cell in that row of the box. The 5 in the third row blocks the bottom row of the box, and the 5 lower down in the third column blocks that column. Only one cell is left, so it must be the 5.
Scanning tip: Work number by number. Look at all the 1s on the board, then check each box that doesn't have a 1 yet. Then do the 2s, and so on. This "cross-hatching" method is the fastest way to find hidden singles.
Naked singles: "only one number for this place"
A naked single is the other way around. Instead of starting from a number, you start from a cell. Look at everything the cell can "see": its row, its column and its box. If eight different numbers are already there, the ninth is the only one left.
Here the centre cell sees 1, 2 and 3 in its row, 4, 5 and 6 in its column, and 7 and 8 in its box. That covers eight numbers, so the answer must be 9.
Naked singles are easy to miss when you are scanning by number, because the clues are spread across three different units. They are much easier to spot once you have notes: any cell with a single candidate written in it is a naked single.
Which one should you look for first?
Most experienced players hunt for hidden singles first, because scanning one number across the whole grid is quick. When that stops producing results, they switch to naked singles, usually by filling in notes. In our game, the hint button checks for hidden singles in boxes, then rows and columns, and then naked singles, which is the same order.
Common mistakes
- Forgetting the box. A number in the same box blocks a cell just as much as a number in the same row or column.
- Trusting old notes. When you place a number, remove it from the notes of every cell in the same row, column and box. Our "Auto-remove notes" setting does this for you.
- Guessing. If you can't find a single, you probably need notes and the next technique, pointing pairs, not a guess.