Is the last empty square the same as a naked single?

It is the simplest case of one. The square can see eight different digits in a single row, column or box, so only one candidate is left. A naked single is the general idea: the eight digits can come from the row, column and box together.

Does it work on other board sizes?

Yes. On a 4×4 every row, column and box holds 1 to 4, on a 6×6 1 to 6, and so on up to 16×16. Whatever the size, a unit with one gap is missing exactly one digit.

What do I do when no row, column or box has just one gap?

Scan instead. Pick a digit and ask where it can go in a box: the copies already on the board rule out rows and columns, and often one square is left. That is lesson 2.

Lesson 1 of 7 · First move

The last empty square: sudoku's easiest move

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Every row, column and box must hold each digit exactly once. So when one of them has eight digits and a single empty square, there is nothing left to decide: the ninth digit is whichever one is missing, and it goes in that square.

Some guides call this a full house or the last digit. It needs no notes and no guessing, which makes it the right first technique to learn, and it is worth checking for whenever a line or box is nearly full.

Example 1: In a row

Step 1 of 3

Row 5 has only one empty square, in column 7.

Row 5 has eight digits: 2, 4, 1, 6, 5, 9, 8 and 7. The one missing is the 3, so the 3 goes in the row's only empty square.

Notice that the square's column and box both still have other gaps, so neither of them could have told you this. The row did.

Example 2: In a box

Step 1 of 3

The bottom-middle box has only one empty square.

The same reasoning works in a box. The bottom-middle box has one empty square, at row 9, column 6, and its eight digits are everything but the 8.

That square's row and column each have more gaps, so here it is the box that decides.

Try it yourself

A new board, and the same idea. Get it wrong and the board tells you why.

Column 6 has only one empty square, ringed. What digit goes there?

Pick the digit for the ringed square.

How to spot it faster

Scan for the fullest rows, columns and boxes first. A line with one gap is easy to miss when you are looking for something cleverer.
Look again after every placement. Each digit you write in can leave another row, column or box one square from complete.

Common mistakes

Counting two gaps as one

Check that the line really has only one empty square. With two gaps there are two missing digits, and either could go in either square until something else decides.

Reading the line instead of counting to 9

Run through 1 to 9 in order rather than reading the line left to right. It is easy to see the 7 you just read and miss that the 4 is absent.

Forgetting columns and boxes

A column or a box with one gap works exactly the same way as a row, and boxes are the ones people forget to check.

Questions

Try it

Play a few easy boards and look for this move before anything else. Solo starts a first visit on an easy 6×6.

Play solo on an easy 6×6