Sudoku Techniques, Step by Step: From Easy to Expert
Every technique you need to solve Sudoku without guessing, with pictures: singles, pencil marks, pointing pairs, naked and hidden pairs, and the X-Wing.
Sunroom Games · Updated
A good Sudoku never asks you to guess. Every square can be worked out from the numbers already on the board — you just need to know where to look. This guide walks through the techniques from the very first one to the ones experts use, with a picture for each.
Every puzzle on Sunroom Games can be solved with the techniques for its level, and no others:
| Level | Techniques you'll need |
|---|---|
| Easy and Medium | The two kinds of single |
| Hard | Singles, plus pointing pairs and naked pairs |
| Expert | All of the above, plus hidden pairs and the X-Wing |
The rule, in one sentence
Fill the board so that every row, every column and every 3 × 3 box contains each of the numbers 1 to 9 exactly once. Everything below follows from that one rule.
1. The only number that fits
Pick an empty square and look along its row, down its column and around its box. Any number you see there can't go in your square. If eight different numbers are ruled out, the ninth must be the answer. Puzzle fans call this a naked single.
This works best on squares with a lot of neighbors already filled in, so start in the busiest row, column or box.
2. The only place it fits
Now turn the question around. Pick a box and a number that's missing from it — say, 5 — and ask: where in this box could the 5 go? Each 5 elsewhere on the board rules out a whole row or column. If only one square is left, the 5 goes there. This is a hidden single.
The same idea works for a row or a column: if a number can only go in one square of a row, it goes there.
Pencil marks: writing down the possibilities
On harder puzzles you'll reach a point where no square has a single answer you can see. That's when pencil marks help. In each empty square, write the small numbers that could still go there. In our Sudoku, tap the Pencil button (or press P on a keyboard), then tap numbers to add or remove them.
Two habits make pencil marks much easier:
- Fill them in one box at a time, checking each number against the row, column and box.
- When you place a number, remove it from the pencil marks in that square's row, column and box. Our game does this for you automatically.
With pencil marks in place, the next techniques become easy to see.
3. Pointing pairs
Sometimes a number can only go in two (or three) squares of a box, and those squares happen to sit in the same row. The number must end up in that row, inside that box — so it can't go anywhere else along that row.
It works the other way round too. If, within a row, a number can only go in squares that all sit inside one box, then that box's copy of the number must be in that row — so you can cross it out of the box's other squares. Either way, look for a number whose possible squares all line up.
4. Naked pairs
If two squares in the same row (or column, or box) can each only be the same two numbers — say 3 or 7 — then those two numbers belong to those two squares. You don't know which way round yet, but you do know that no other square in that row can be a 3 or a 7.
After the clean-up, look again: crossing out numbers often leaves a square with a single possibility.
5. Hidden pairs
This is the naked pair turned inside out. Look at where each missing number could go in a row. If two numbers can each only go in the same two squares, those squares must hold those two numbers — so any other pencil marks in them can be crossed out.
Hidden pairs are harder to spot than naked ones because the pair is buried among other pencil marks. A good way to find them is to go through the missing numbers one at a time and count how many squares each could go in. Two numbers with the same two squares are your pair.
6. The X-Wing
The X-Wing sounds intimidating, but it's the pointing pair idea applied to two rows at once. Choose a number and find two rows where it can only go in two squares — and the two squares are in the same two columns in both rows. The four squares form a rectangle.
The number has to go in opposite corners of that rectangle: one in each row, and one in each column. Either way, both columns get their copy of the number from those rows, so it can be crossed out everywhere else in those two columns.
The same pattern works with columns in place of rows. You'll rarely need it, but when an Expert puzzle seems completely stuck, an X-Wing is often hiding in plain sight.
A routine that solves almost anything
- Scan for hidden singles, number by number, in every box.
- Check the busiest squares for naked singles.
- When those run out, fill in pencil marks.
- Look for pointing pairs and naked pairs, clean up, and go back to step 1.
- On Expert puzzles, look for hidden pairs and X-Wings when everything else is stuck.
And if you're stuck anyway, ask for a hint. Our Sudoku first checks whether any square has a mistake in it. If not, it shows you a square you can fill with one of the two singles and explains why, in the same words this guide uses. When the next step needs one of the harder techniques, it fills a square in for you instead.