Sudoku techniques for beginners
Learn scanning, naked and hidden singles, pencil marks and naked pairs, and practise on small 4 × 4 and 6 × 6 grids before moving on.
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A sudoku fills a grid so that every row, column and box contains each digit exactly once. Beginners often guess, but most puzzles can be solved with a few logical techniques. The ones below are the most useful. You can practise them on Paperoom's sudoku maker.
Start with a small grid
A 4 × 4 grid uses 2 × 2 boxes and the digits 1 to 4. A 6 × 6 grid uses boxes of 2 rows by 3 columns and the digits 1 to 6. Smaller grids have fewer possible digits in each cell, so the techniques are easier to see. Practise on these before moving to a 9 × 9 grid.
Scan with cross-hatching
Scanning, also called cross-hatching, is the technique most players learn first.
- Choose a digit, such as 5.
- Choose a box that does not yet contain a 5.
- Look at the rows and columns that cross that box. If a row or column outside the box already holds a 5, that line cannot hold a 5 inside this box.
- If only one cell in the box is still possible, write the 5 there.
- Repeat for each digit and each box.
Find naked singles
A naked single is a cell where only one digit fits, after you have checked its row, column and box. It is the simplest find in sudoku.
When you find one, write the digit in the cell, then erase that digit from the pencil marks in the same row, column and box. Each placed digit can reveal another single, so keep scanning after every placement.
Find hidden singles
A hidden single is a digit that fits in only one cell of a row, column or box, even if that cell also has other possibilities. Hidden singles are easy to miss because the cell looks crowded.
For each missing digit, scan one row, then one column, then one box, and ask "where can this digit go?" If only one cell is left, the digit belongs there.
Tip: Look at the digit, not the cell. Checking one digit at a time across the whole grid is often easier than checking each cell in turn.
Use pencil marks
Pencil marks are small notes of the digits that could still go in a cell. Write them in pencil, and erase a mark whenever you place a digit that rules it out. Mark a few cells at a time, or work one box at a time, so the notes stay manageable.
Spot naked pairs
A naked pair is two cells in the same row, column or box that contain only the same two candidates, for example 3 and 7. One of those cells must hold 3 and the other must hold 7. That means neither digit can go in any other cell of that row, column or box, so you can erase both from the other pencil marks in that unit.
Naked pairs take practice to spot. Start by looking for cells with only two marks in each.
Check your work
Before you finish, check each row, column and box once more. Every one should hold the digits 1 to 9 exactly once, or the digits 1 to 4 or 1 to 6 on a smaller grid. A single repeated digit is the usual sign that one earlier placement went wrong, so trace back through the last few digits you wrote.
Know when to take a break
If you are stuck, stop for a few minutes and come back with fresh eyes. Many players find they then spot a single they missed earlier. Avoid guessing. If you must try a digit, write it in pencil, and erase it if the grid later contradicts it.
Working on a small grid first, then stepping up, is a sensible way to build confidence. Each technique is easier to spot once you have used it several times.
