Logic Puzzle Club /

Naked singles: the only digit left

Cross off every digit a cell can see. When one is left, that is the answer. This is elimination.

6

123456

3

2

4

5

6

3

1

2

5

2

Pick an empty cell. Row 1, column 3 could be any digit from 1 to 6.

1 of 5

How it works

Every empty cell starts with a list of candidates: the digits it could still be. In a 6×6, that is 1 to 6.

Now apply the rules. The cell’s row already has some digits, and a row holds each digit at most once, so the cell can’t be any of them. The same goes for its column and its box. Cross them all off.

If one candidate is left, the cell must be that digit, because every cell holds a digit. That cell is a naked single. The reasoning is elimination: rule out every option but one.

Why it is a proof

Each cross-off is a small argument. Row 1 has a 6. If this cell were 6, row 1 would have two 6s. It can’t, so this cell is not 6. That is modus tollens: if P then Q, not Q, so not P.

Then the last step: the cell is 1, 2, 3, 4, 5 or 6. It is not 2, 3, 4, 5 or 6. So it is 1. That is elimination, and it is as certain as the rules.

How to scan for them

You don’t need to pencil every cell. Look for cells in a busy row, column and box. Count the different digits they see. A 6×6 cell that sees five different digits is a naked single.

Worth memorizing

A naked single is a cell with one candidate left.
Look at the row, the column and the box.
Every digit in them is off the list.
A cell that sees every digit but one is solved.
In a 6×6, that means five different digits.

Practice

0 of 5 right

Question 1

6

3

2

4

5

6

3

1

2

5

2

What goes in the ringed cell?

Question 2

6

1

3

2

4

5

6

3

1

2

5

2

With the 1 placed, what goes in the ringed cell?

Question 3

1

3

1

2

3

6

4

5

6

5

1

Which of these cells is a naked single?

Question 4

1

3

1

2

3

6

4

5

6

5

1

How many candidates does the ringed cell have?

Question 5

1

3

1

2

3

6

4

5

6

5

1

What goes in the ringed cell?

Where you’ll use this

EliminationThe logic behind every cross-off Sudoku’s rulesThe sentences you are quoting Play sudokuFind a naked single in today’s puzzle

Play today’s sudokuPut this lesson to work Next: Hidden singles: the only place leftPick a row and a digit it still needs. If only one cell can take it, it goes there. This is “exactly one” at work.