Sudoku strategy, one technique at a time
Every Sudoku can be solved with a small set of patterns. This page covers eight of them, in the order you are likely to need them.
The first two will finish most Easy and Medium puzzles. The rest come into play on Hard and above. You do not need to learn them all at once. Get comfortable with one, then add the next when a puzzle leaves you stuck.
| Technique | First needed on | What to look for |
|---|---|---|
| Naked single | Easy | A square with only one possible number |
| Hidden single | Easy | A number that fits only one square in a unit |
| Naked pair | Hard | Two squares that share the same two options |
| Hidden pair | Hard | Two numbers that fit only the same two squares |
| Pointing pair | Expert | A number stuck in one row or column of a box |
| Box and line reduction | Expert | A number stuck in one box within a row or column |
| Naked triple | Master | Three squares that share three options between them |
| X-Wing | Master | A number locked into a rectangle across two rows |
A quick word on terms: a unit is any row, column or box, and a candidate is a number that could still go in a square. The how to play guide explains the rest.
1. Naked single
Look at one empty square and check its row, its column and its box. If eight of the nine numbers already appear across those three units, the ninth is the only one left. It goes in.
Naked singles are easiest to spot in busy parts of the board, where a square is surrounded by filled rows and columns. On this site, selecting a square shades its row, column and box, which makes this check quick.
2. Hidden single
Now turn the question around. Instead of asking which numbers fit a square, ask where a number can go in a unit. Take the number 3 and one box that does not have a 3 yet. If every other empty square in that box is blocked by a 3 in the same row or column, only one square is left.
The square might have several candidates, which is why this pattern is called hidden. It is the move behind most scanning, and it is the single most useful technique in the game.
3. Naked pair
Suppose two squares in the same row both have exactly the candidates 4 and 7, and nothing else. You do not know yet which is which, but you do know that the 4 and the 7 for that row are used up by those two squares. So you can remove 4 and 7 from the notes of every other square in the row.
The same works in a column or a box. If the two squares share a box and a row, you can clear both. Removing candidates often turns a neighbouring square into a naked single.
4. Hidden pair
This is the naked pair turned around. Say that in one column the numbers 2 and 9 can each only go in the same two squares. Those two squares must hold 2 and 9, so any other candidates in them can be deleted. After the clean up, the pair is naked and easy to see.
Hidden pairs are harder to notice because the squares still look busy. A good habit is to check each number that appears only twice in a unit.
5. Pointing pair
Look at one box and one number. If every place that number can go in the box lies in the same row, then the number has to be in that row within this box. That means it cannot be anywhere else in the same row outside the box.
For example, if the only spots for a 5 in the top left box are both in row 2, you can remove 5 from row 2 in the top middle and top right boxes. The two squares point along the row, which gives the technique its name. It works with columns too, and with three squares instead of two.
6. Box and line reduction
This is the pointing pair seen from the other side. If, in one row, every place a number can go falls inside a single box, the number must be in that part of the row. So it cannot go anywhere else in that box.
Say the only spots for an 8 in row 5 are in the middle box. Then the 8 of the middle box is in row 5, and you can remove 8 from rows 4 and 6 of that box.
7. Naked triple
A naked triple is three squares in one unit whose candidates, taken together, are only three numbers. The squares do not each need all three. Candidates of 1 and 6, 6 and 8, and 1 and 8 form a triple, because between them they only use 1, 6 and 8.
As with the pair, those three numbers are used up by those three squares, so remove them from every other square in the unit. Quads exist too, but they are rare and hard to spot by eye.
8. X-Wing
The X-Wing is the first technique that looks at two rows at once. Pick a number, say 2. Find two rows where the 2 can only go in two squares, and where those squares sit in the same two columns. The four squares form the corners of a rectangle.
In each of the two rows the 2 must go in one of its two corners, and the corners on the same diagonal go together. Either way, each of the two columns gets exactly one of these 2s. So no other square in those two columns can hold a 2, and you can remove it from all of them.
The same logic works with columns swapped for rows. Its bigger cousin, the Swordfish, uses three rows and three columns. You will meet it now and then on Extreme.
When you are completely stuck
- Check your notes. Most stalls come from a note that should have been removed. Update the notes around the last few numbers you placed.
- Go number by number. Pick the number that appears most often on the board and look for hidden singles with it. Then the next most common.
- Count the candidates. Squares with two candidates are where pairs, triples and X-Wings start.
- Take a break. Use Pause. A fresh look finds more than another ten minutes of staring.
- Use one hint. A hint fills the square with the fewest options, so it usually shows you the next thing a good solver would have found.
Practise one technique at a time on a level that suits it. Hidden singles on Medium, pairs on Hard, pointing pairs and box and line checks on Expert. Start a puzzle and try it.