Sudoku strategies

Every puzzle in Sudoku Arena can be solved by logic alone. The harder the level, the more advanced the technique you will eventually need. This guide goes from the techniques that solve every Easy puzzle to the ones you need for Extreme. If you are new to Sudoku, read how to play first.

Words used below: a unit is any row, column or box. A candidate is a number that could still go in a cell. Writing candidates as notes makes every technique after the first two much easier to spot.

1. Naked single

A cell where only one number is possible. Look at everything already in the cell's row, column and box; if eight different numbers appear there, the ninth number goes in the cell.

Where to look: cells in crowded rows, columns and boxes, especially where a busy row crosses a busy column.

2. Hidden single

A number that has only one possible place in a unit, even though that cell may have other candidates too. For example, if the 5s in neighbouring rows and columns rule out every cell of a box except one, the 5 must go there.

How to find them: pick a number, then go box by box (cross-hatching), asking "where can this number go?". Easy and Medium puzzles are solved entirely with naked and hidden singles.

3. Pointing pair (and triple)

Inside one box, a candidate is limited to two or three cells that all lie in the same row (or column). Whichever of those cells it ends up in, that row inside the box will hold the number, so you can remove that candidate from the rest of the row outside the box.

This is often the first technique you need on Hard puzzles. It does not place a number straight away; it removes candidates, which usually creates a new single.

4. Box/line reduction

The reverse of a pointing pair. If, in a row, a candidate can only appear in cells that are all inside the same box, then the number must be in that part of the box, so remove it from the other cells of that box.

5. Naked pair, triple and quad

Two cells in the same unit that each contain only the same two candidates, for example {3, 8} and {3, 8}. One cell will be 3 and the other 8, so no other cell in that unit can be 3 or 8. Remove those candidates everywhere else in the unit.

The same idea works with three cells sharing three candidates (a naked triple, such as {1,4}, {4,9}, {1,9}) or four cells sharing four. The cells do not each need all the numbers; together they must use exactly that many.

6. Hidden pair and triple

Two numbers that, within a unit, can only go in the same two cells. Those two cells must hold those two numbers, so every other candidate in those two cells can be removed. Hidden pairs are harder to see than naked ones because the cells are cluttered with other notes. They are the signature technique of Master puzzles.

7. X-Wing

Take one number. If, in two different rows, it can only go in the same two columns, those four cells form a rectangle. The number must sit in opposite corners of it, one in each row, so it occupies both columns. You can therefore remove that number from every other cell in those two columns. The same works with columns and rows swapped.

8. Swordfish

An X-Wing with three rows and three columns. If in three rows a number is limited to cells in the same three columns (each row having two or three of them), the number is locked into those columns, so remove it from the rest of those three columns.

9. XY-Wing

Three cells with two candidates each. A "pivot" cell {X, Y} sees two "pincer" cells, {X, Z} and {Y, Z}. Whatever the pivot turns out to be, one of the pincers must be Z. So any cell that sees both pincers cannot be Z. XY-Wings, X-Wings and Swordfish are what make Extreme puzzles extreme.

Which technique for which level?

When you are stuck

1. Re-scan every number from 1 to 9 for hidden singles. It is the most commonly missed move.
2. Fill in all candidates if you have not already, then look for pairs.
3. Check boxes for pointing pairs; they often unlock a whole region.
4. Use a hint. In Sudoku Arena a hint shows the cell and names the technique that proves it, which is a good way to learn a new one.

Put it into practice: play an Expert puzzle or take on the Daily Challenge.