Naked single: the last possible number in a cell
Updated
You’ve filled a few cells, but row 4 still has several gaps. One of them can take only 7. That’s a naked single: the row, column, and box have ruled out everything else.
You are asking what this cell may hold. You are not yet asking where a particular digit wants to live.
When to use it
Start here. You can see it without pencil marks, once eight different digits have shown up around the cell. If you have written notes, the list has shrunk to one digit. Place it.
On Calmtile, Easy puzzles are finished with this check and with hidden singles. This page does not need pairs or pointing.
Where to look
Stay on one empty cell. Gather the digits already written in its row, its column, and its 3 by 3 box. Anything that appears in those three places is finished for this cell. Eight different digits, and the missing one is the answer.
The example cell is r4c4, in the center box. Row 4 already holds 1, 2, 3, 8, and 9. Column 4 holds 4, 5, and 6. The rest of the center box is empty, so it adds nothing. Those eight digits leave 7.
Row 4 is not down to its last empty square. I used to stare at the last hole in a row and call it this. r4c5, r4c6, and r4c9 are still open, and each of them can hold more than one digit. The single belongs to r4c4 alone.
The step
- Choose an empty cell.
- List the digits in its row, its column, and its box.
- When eight different digits are present, place the one that is missing.
- When the list is shorter, leave the cell. Look at another, or go on to the next check.
Placing the 7 is the whole step. You do not first erase a candidate somewhere else. After the 7 is in r4c4, every other cell that shares its row, column, or box simply cannot be 7. The other empty cells stay empty. They are not singles yet.
Example
Row 4 still has empty cells. r4c4 can only be 7.
r4c4 sees 1, 2, 3, 4, 5, 6, 8, and 9. The digit left standing is 7. The mark in the cell is that one candidate, not a guess.
Easy to misread
A row with a single hole is often easy, because that hole can see the row. It is a naked single only when the column and the box, counted with the row, leave one digit. A digit with one home left in a row, column, or box is a different fact. That is a hidden single, on the next page.
Two candidates is not a single either. A short list is something you may write down. It is not a cell you fill.
Next
Next time a cell goes this quiet, try the row, the column, and the box before you look for anything fancier. The other easy check is the hidden single. Where these two sit among the grades is on easy, medium, hard and expert Sudoku.