How to solve a Sudoku: the two moves that solve most puzzles

To solve a Sudoku, fill the grid so that every row, every column and every 3 by 3 box holds the digits 1 to 9 exactly once. You never have to guess: every Gridarium puzzle has exactly one solution, and Easy, Medium and Hard puzzles can all be solved by reasoning alone with the moves below. Expert puzzles may ask for a little more.

Move 1: the cell that can only be one digit

Pick an empty cell and look along its row, its column and its box. Together they already contain some digits. If eight different digits are there, the cell can only be the ninth.

On the grid below, which is the Easy puzzle of Tuesday, October 20, look at the highlighted cell (row 1, column 8). Between its row, its column and its box it already sees 1, 2, 3, 4, 5, 7, 8, 9. That leaves one digit: 6.

Move 2: the digit that has only one place to go

Now turn it around. Pick a digit and a row, a column or a box. Which empty cells there can still take that digit? If there is only one, that is where it goes, even if that cell could also hold other digits.

On the same grid, look at row 2, which is highlighted. Every other empty cell in it already has a 3 somewhere on its own row, column or box, so the 3 can only go in one place: row 2, column 2.

Write the possibilities down

When you cannot see a move, note the digits each empty cell could still take. In Gridarium, the Notes button does this, and a note disappears by itself when you place that digit anywhere on its row, column or box. Most of the time, a cell with a single note left is Move 1, and a digit noted in only one cell of a row is Move 2.

When you are stuck: two more ideas

• Two cells in the same row, column or box that can only hold the same two digits (say 4 and 7) must take those two digits between them. So 4 and 7 can be crossed off every other cell of that row, column or box.
• If, inside a box, a digit can only go in cells of one row, then that digit belongs to that row, and you can cross it off the rest of the row outside the box. It works the same with columns.

What the levels mean on Gridarium

• Easy: only Move 1. The puzzle keeps at least 40 digits already placed.
• Medium: Move 1 and Move 2. At least 34 digits are placed.
• Hard: also the two ideas above, crossing off digits with pairs and locked candidates. At least 28 digits are placed.
• Expert: may need hidden pairs, or trial and error. Expert is a Premium level.

The puzzle of the day follows the week: easy on Monday and Tuesday, medium on Wednesday and Thursday, hard from Friday to Sunday.