Naked Single (Obvious Single)
Used in Classic 9×9 Sudoku, 6×6 Sudoku, Difference Sudoku, Irregular 6×6 Sudoku, Relational 6×6 Sudoku, Odd/Even Sudoku, Windowed Sudoku, Killer Sudoku, Skyscraper Sudoku 5×5 and Triangle Sudoku.
A naked single is a cell with only one candidate left. Every other digit is already in its row, its column or its box, so the one that remains must go there. It is the first technique anyone learns, and on an easy puzzle it does most of the work.
An example
Take the cell in the seventh row, second column. Count what can't go there:
- Its row already has 2, 4, 5 and 9.
- Its column already has 6, 7 and 8.
- Its box, the bottom-left one, has 1, 2, 4 and 8.
Put together, that rules out 1, 2, 4, 5, 6, 7, 8 and 9. Only 3 is left, so the cell is 3.
How to look for them
There are two ways to find naked singles, and good solvers switch between them.
- Look for crowded cells. A cell whose row, column and box are all well filled has the fewest options. Check each of the three for the digits it already holds, and see whether anything is left out.
- Use notes. Once every empty cell has its candidates written in, a naked single is simply a cell with one small digit in it. The Fill Notes button in the More menu fills them all in for you, and by default placing a digit clears it from the notes of the cells it affects, so new singles show up as you go.
Placing a single often creates the next one. The digit you just placed is gone from every cell in its row, column and box, so look there first.
Naked or hidden?
The name says how you find it. A naked single is a cell with one possible digit: you look at the cell and see the answer. A hidden single is a digit with one possible cell in a row, column or box: the cell may still have several candidates, and you only see the answer by asking where the digit can go. The app's hints call the first an "Obvious single".
Puzzles graded Easy here can be finished with these two techniques alone. When neither moves, the next step is to look for naked pairs.
In the variants
Every variant on this site uses naked singles, because every one of them is built on rows and columns that hold each digit once. The variant's own clues add more ways to rule digits out: a killer cage's total, a skyscraper's view count, a greater-than sign. Whatever rules a digit out, the step at the end is the same: one candidate left, so it goes in.
More techniques
- Hidden Single: When a digit fits in only one cell of a row, column or box, it goes there, even if that cell has other candidates.
- Naked Pair (Obvious Pair): Two cells in a house with the same two candidates take both digits between them, so the rest of the house can't have either.
- Naked Triple (Obvious Triple): Three cells in a house whose candidates use only three digits take all three, even when no cell shows all of them.
- Hidden Pair: Two digits that fit in only the same two cells of a house claim those cells, so every other candidate there can go.
- Hidden Triple: Three digits confined to the same three cells of a house claim them, clearing out every other candidate in those cells.
- Pointing Pairs and Triples: A digit confined to one line inside a box (or to one box along a line) can be removed from the rest of that line or box.