How to solve sudoku: a beginner’s guide
Every sudoku can be solved by logic alone, with no guessing. These five techniques are enough for most easy and medium puzzles.
The rules
Fill the 9×9 grid so that every row, every column and every 3×3 box contains each digit from 1 to 9 exactly once. The starting digits never change, and a good puzzle has only one solution.
A row with eight digits already placed: 2 is the only digit missing, so the last cell must be 2.
1. Scan for the easy cells first
Pick a digit, say 1, and look at where it already appears. Each 1 rules out its whole row, column and box. If that leaves only one empty cell for 1 in some box, place it. Then do the same for 2, 3 and so on. Starting with digits that already appear often is quickest.
2. Naked single: the only digit that fits a cell
Look at one empty cell and list the digits already used in its row, column and box. If eight different digits are ruled out, the ninth must go there. This is the most common move in easy puzzles.
3. Hidden single: the only place for a digit
Sometimes a cell could hold several digits, but within its row, column or box there is only one cell where a particular digit can go. That digit goes there, even though the cell had other options. Look for these inside boxes first: they are the easiest to spot.
4. Pencil marks
When the easy moves run out, write the possible digits in small numbers in each empty cell (most apps call this notes or pencil mode). Update the notes each time you place a digit. Notes make the next two techniques visible.
5. Pairs and pointing
Naked pair
If two cells in the same row, column or box can only be the same two digits, say 4 and 7, then those two digits must go in those two cells. Remove 4 and 7 from the notes of every other cell in that row, column or box.
Pointing
If, inside one box, a digit can only go in cells that lie in a single row, that digit must be in that row within this box. So you can remove it from the rest of that row outside the box. The same works for columns.
A routine that works
- Scan digits 1 to 9 for hidden singles in each box.
- Check rows and columns that are nearly full for naked singles.
- When stuck, add pencil marks and look for pairs and pointing.
- After every new digit, go back to step 1: one placement often unlocks several more.
Harder techniques, for later
Expert puzzles need patterns such as X-Wing (one digit limited to the same two columns in two rows) and Swordfish. Learn them once the five techniques above feel automatic.
Play today’s free sudokuEasy to expert, a new puzzle every day, with notes mode.Like logic puzzles? Try Nonogram, where you shade cells from number clues to reveal a picture.