Helpful Sudoku

Work through a deduction

Three ways to find a forced move

A single is a move you can justify without trying a guess. The diagrams below show what to look for and why the move follows.

Each diagram isolates one group of nine cells. Large single digits are already placed; comma-separated digits are candidates after checking the other groups. These are teaching examples, not complete playable grids. On a full board, always check the row, column and box—and the diagonals when playing X Sudoku.

1. Naked single: what can this cell contain?

1234567?9
A row with one empty cell: the outlined eighth cell must be 8.

This row already contains 1, 2, 3, 4, 5, 6, 7 and 9. Sudoku requires each digit from 1 to 9 exactly once in the row. The only missing digit is 8, so enter 8 in the eighth cell.

This is the simplest naked single. A row does not have to be almost full: the row, column and box can rule out different digits, leaving just one candidate when their restrictions are combined.

After the move: remove 8 from the candidates of other empty cells sharing its row, column or box. That may expose another single. If your candidate list becomes empty, revisit an earlier entry or a crossed-out mark.

2. Hidden single: where can this digit go?

1346792, 52, 5, 82, 5
Row candidates: only the outlined eighth cell includes 8.

The row is missing 2, 5 and 8. None of its three empty cells has just one candidate, so a search for naked singles finds nothing here. Instead, track the missing digit 8 across the row.

The seventh and ninth cells cannot contain 8. The eighth cell is its only possible home. Enter 8 there and remove the 2 and 5 notes from that cell. The two remaining cells still each allow 2 or 5; this deduction does not decide between them.

Why “hidden”? The forced digit was mixed in with other pencil marks. Those other marks were locally legal, but the requirement to place an 8 somewhere in the row rules them out in this cell.

Try the same search in a box: pick a digit missing from the box and count the cells whose candidate lists include it. Exactly one means a hidden single. Two or more means this test alone has not found a move.

3. X Sudoku: use the extra groups

1245673, 93, 8, 93, 9
An X Sudoku diagonal, read from one corner to the other: only its eighth cell can be 8.

Imagine these cells along the long diagonal from the top-left to the bottom-right corner. X Sudoku requires this diagonal to contain every digit exactly once, just like a row. It is missing 3, 8 and 9.

Only the eighth diagonal cell includes 8 in its candidates. It must be 8: a hidden single on a diagonal. On the full grid this is row 8, column 8. The same reasoning works on the other long diagonal.

After placing it: update its row, column, box and diagonal. The centre cell belongs to both diagonals, so a number entered in the centre affects both. These diagonal restrictions apply only to X Sudoku, not classic Sudoku.

Practise finding the move yourself

  1. Start with a printed Easy puzzle with candidates, or open an Easy game with singles highlighting off.
  2. Look for a cell with one candidate. Say which groups ruled out the other digits before you fill it.
  3. If none stands out, choose a missing digit in a row, column or box and count its possible positions.
  4. Enter a forced digit, update the affected notes, then look again.

A cell with several candidates is not automatically a reason to guess. It may contain a hidden single, or need a more advanced deduction. If you get stuck in the game, ask for a Hint and read the explanation before entering its suggested digit.

Read the candidates and contradictions guide or try the ideas in a game.