How to Use Sudoku Candidate Notes

What are candidates?

In “Finding your first number ①” in Sudoku Rules: A 3-Minute Guide, you picked an empty cell and ruled out every number already in its row, column and 3×3 box. The numbers left are that cell's candidates. If only one candidate remains, it is the answer. If two or more remain, you cannot decide yet.

In a difficult puzzle, most empty cells have two or more candidates. Writing them in small figures in each cell lets you see relationships you might miss when keeping them in your head. In this article, cell positions are again written as r3c5 (row 3, column 5).

How to write candidates in this app

• Turn on the Notes button above the number pad (or press N on your keyboard), select a cell and press a number to write it in small figures inside the cell. Press the same number again to remove it.
• Notes are not answers, so they do not count toward Mistakes. If you are unsure about a number, leave it as a note instead of entering it as an answer.
• When Auto-remove notes is enabled in settings (the default), entering a correct number removes notes for that number from the same row, column and box.

When should you use them?

You can often finish an easy puzzle with many givens using just the two methods in the rules article, so you do not need candidates in every cell. Start writing them when alternating between those two methods no longer gives you another number.

To avoid missing candidates, work through one row, column or box at a time. For example, select the empty cells in column 1 from top to bottom, checking each cell's row, column and box and writing down every number that remains.

Finding a number with candidates — two cells with the same two numbers (Naked Pair)

In the example below, the two methods from the rules article cannot fill any more cells. Here are the candidates for the empty cells in column 1.

c1c2c3c4c5c6c7c8c9

r1r2r3r4r5r6r7r8r9

469

5

3

2

8

1

13469

8

5

2

12346

7

8

5

9

69

8

2

3

5

1

4

5

7

1

8

9

4

2

6

3

69

4

3

2

1

5

8

8

5

9

2

4

6

23

1

4

5

8

6

7

7

6

8

5

• r4c1 has only 6 and 9 as candidates: row 4 contains 1, 2, 3, 4, 5 and 8, and box 4 contains 7.
• r6c1, checked the same way, also has only 6 and 9 as candidates.

Both cells are in column 1, and both have exactly the same two candidates, 6 and 9. You do not yet know which cell is 6 and which is 9, but column 1's 6 and 9 must occupy these two cells. No other cell in column 1 can therefore contain either number.

Remove 6 and 9 from r1c1's candidates of 4, 6 and 9, and only 4 remains. So r1c1 must be 4. The candidates in r2c1 and r3c1 also shrink, making your next number easier to find.

When two cells in one row, column or box have exactly the same two candidates, you can remove those numbers from the other cells in that row, column or box. This technique is commonly called a “Naked Pair.”

When you cannot use this method

• Both cells must have exactly the same two candidates. If one has an extra number, as in {6, 9} and {4, 6, 9}, it is not a Naked Pair.
• Both cells must be in the same row, column or box, and you can remove candidates only from other cells in that shared area. In the example, r4c1 and r6c1 also share box 4, but that box has no other empty cells, so there is nothing more to remove there.
• If you have left out even one candidate, what looks like a Naked Pair may not be one. Double-check both cells' candidates before using the pair.

Common mistakes

• You leave out a candidate. Removing numbers because of a false pair created by a missing candidate will eventually lead you to a wrong answer. Check the row, column and box before writing a cell's candidates.
• You leave nearby notes unchanged after entering a number. Outdated notes can make you see pairs that do not exist. Keeping Auto-remove notes enabled helps reduce this problem.
• You mix guesses into your notes. “This is probably the number” is not a candidate. Only note numbers that the rules do not let you rule out.

Practice puzzle

c1c2c3c4c5c6c7c8c9

r1r2r3r4r5r6r7r8r9

4

7

6

5

4

2

6

6

9

1

4

6

8

1

4

3

8

7

6

1

3

6

5

8

1248

12348

123

29

7

6

239

5

29

6

9

8

3

1

4

1

6

8

What number goes in r7c7? Find the two cells in row 7 with exactly the same candidates.

Show answer

3. Both r7c4 and r7c9 have candidates {2, 9}, so row 7's 2 and 9 must occupy those two cells. Removing 2 and 9 from r7c7's candidates of 2, 3 and 9 leaves only 3. For the same reason, you can also remove 2 from the candidates in r7c1, r7c2 and r7c3.