Sudoku is a logic puzzle, not a maths puzzle. You never add anything up. The numbers one to nine are simply nine different symbols, and your job is to place them in a nine-by-nine grid so that no symbol repeats in any row, column or three-by-three box. The puzzle gives you a few starting symbols and promises that exactly one solution exists. This guide teaches the techniques in the order you are likely to need them, using the daily Sudoku on OnlinePlayZone for practice.
Start with scanning
Scanning is the simplest technique and it solves most easy puzzles. Pick a number, say seven, and look at the grid. Wherever a seven already sits, it rules out its entire row, column and box for another seven. Take a box that does not yet have a seven. Cross out every row and column that already has one, and often only one cell in the box remains. That cell must hold the seven.
Work through the numbers one to nine, then repeat. Each placement creates new restrictions, so a second pass will find numbers the first pass could not. Beginners who simply scan patiently, one digit at a time, can finish easy puzzles without any other tool.
Count what is missing
A second easy technique is counting. Find a row, column or box that is nearly full, for example one that has seven of its nine numbers. Work out which two are missing and see which cell can hold each. Because the nearly full unit offers only a couple of candidates, you can often decide the answer immediately.
Naked singles
When scanning stops working, start writing candidates. In each empty cell, jot down the numbers that could still legally go there. A cell with only one candidate is called a naked single: the cell has only one number it can hold, so you place it. This sounds trivial, but when you update candidates after each placement, naked singles keep appearing and often carry you through medium puzzles.
Hidden singles
A hidden single is the same idea seen from the other direction. Look at a row, a column or a box and ask: where can the five go? If only one cell in that unit lists a five among its candidates, then the five has to go there, even if that cell has other candidates too. You place the five and erase the other candidates in that cell. Hidden singles are the most useful intermediate technique, and many puzzles that look impossible fall apart once you look for them systematically.
Naked pairs
Now the patterns. Suppose two cells in the same unit, both containing only the candidates three and eight, appear in a row. Those two cells must hold the three and the eight between them, in some order. That means no other cell in the row can hold a three or an eight, so you can erase those candidates from the rest of the row. This is a naked pair. It does not place a number directly, but each removed candidate makes other cells simpler, and the effect often triggers a chain of new singles.
The same idea works with triples, three cells that share three candidates, although they are harder to spot.
Hidden pairs
A hidden pair is the mirror image. Imagine that in a column the numbers two and six appear as candidates in exactly two cells, and nowhere else in that column. Those two cells must hold the two and the six, so you can erase every other candidate from those two cells. The cells might have had five candidates each; after the hidden pair is found they have two.
Pointing pairs and box-line reduction
Sometimes, within a box, all the candidates for a number sit in one row. That means that the number must go in that row within that box, so it cannot go anywhere else in the same row outside the box. You can erase it from the rest of the row. This is a pointing pair or triple. The reverse also works: if within a row all candidates for a number sit inside one box, that number cannot appear elsewhere in the box.
X-wing, the first advanced pattern
An X-wing needs a particular shape. Look for a number that appears as a candidate in exactly two cells in each of two different rows, and the four cells line up in the same two columns, forming a rectangle. The number must occupy one diagonal of that rectangle. Whichever diagonal it is, the two columns each receive that number from the rectangle, so you can remove it from every other cell in those two columns. X-wings are rarer than pairs, but they unlock the toughest puzzles.
A routine that works
- Scan the grid for easy placements, one number at a time.
- Fill in the candidates in every empty cell.
- Look for naked singles, then hidden singles.
- Look for pairs, then pointing pairs.
- Only after all of that, try X-wing.
- After every placement, update candidates, then go back to step three.
Common mistakes
The most common mistake is a wrong placement that does not show up until much later, when a row has no place for a number. To prevent it, double-check each placement against its row, column and box. A second mistake is forgetting to update the candidates after a placement. Third, solving by guesswork: if you notice yourself thinking "it might be a four", stop and look for a technique instead.
Practise every day
Sudoku improves quickly with regular practice. The daily puzzle on OnlinePlayZone is the same for every player on a given date, so it gives you a fresh challenge each day and a streak to protect. Try to solve it without hints first. If you get stuck, find the technique that would have unblocked you, then use it on the next puzzle.
Frequently asked questions
Do I ever need to guess in Sudoku?
A well-made puzzle can always be solved by logic alone. If you feel you must guess, there is usually a technique you have not looked for yet, such as a hidden single or a naked pair.
Should I write candidate numbers in the cells?
Yes, once the easy numbers run out. Candidate notes make patterns such as pairs and triples visible and are the basis of every intermediate technique.
How long should a Sudoku take?
Beginners often need 15 to 30 minutes on an easy puzzle. With practice, easy puzzles take a few minutes and medium puzzles around 10 minutes.
