Sudoku techniques, from singles to the X-Wing
The Sudoku techniques worth learning, in the order you will need them, are the naked single, the hidden single, the naked pair, pointing and the X-Wing. The first two place digits and are enough for many easy puzzles. Pairs and pointing remove candidates on harder ones. The X-Wing is the first pattern that spans the whole grid.
| Technique | What you look for | When you need it |
|---|---|---|
| Naked single | A square where only one digit fits | Every puzzle |
| Hidden single | A digit with only one place left in a row, column or box | Every puzzle |
| Naked pair | Two squares in one unit that share the same two candidates | Medium puzzles |
| Pointing | A digit whose places in a box all sit in one row or column | Medium to hard |
| X-Wing | One digit with two places in each of two rows, in the same two columns | Hard puzzles |
1. Naked single
A square where only one digit is still possible. Look at everything in its row, its column and its box. If eight digits are ruled out, write the ninth.
2. Hidden single
A digit that has only one possible square left in a row, a column or a box. That square may have several candidates, but the digit has nowhere else to go, so it goes there.
Check every digit in every box, then in every row and column. Hidden singles are easy to miss.
3. Naked pair
Two squares in the same row, column or box that can each hold only the same two digits. Between them they must take those two digits, in one order or the other, so no other square in that row, column or box can hold either.
In row 1, the two empty squares of the first box can only be 4 or 9. Whichever way round they go, 4 and 9 are used up in that row, so they come off every other empty square of the row. The same works with three squares that share three digits, a naked triple.
4. Pointing
Look inside one box at one digit. If every square where that digit can still go lies in the same row, the digit must land in that row inside this box. So it cannot go anywhere else in that row. The same is true for a column.
In the top-left box, 6 can only go in two squares, and both are in row 2. Row 2's 6 is therefore inside this box, and 6 comes off the rest of row 2.
5. X-Wing
Pick one digit. If in two different rows it has exactly two possible squares each, and those squares sit in the same two columns, the four squares make a rectangle. The digit must take two opposite corners of it, so each of those two columns gets the digit in one of those two rows. Every other square in the two columns loses the digit as a candidate.
In rows 2 and 7, the digit 2 can only go in columns 3 and 8. Whichever diagonal it takes, columns 3 and 8 get their 2 from these rows, so 2 comes off every other square of columns 3 and 8. The pattern works the same way with rows and columns swapped.
Tips that save time
- Scan by digit, not by square: take one digit and sweep all nine boxes for it.
- Update pencil marks the moment you place a digit, or they will mislead you.
- When you are stuck, look for pairs and pointing before anything rarer.
- Do not guess. If a proper Sudoku seems to need a guess, a candidate somewhere is wrong.
The same habit in Light Up
Pointing has a twin in Light Up. If every square that could light a dark square lies in one courtyard, that courtyard's lantern must be one of them, and the rest of the courtyard is crossed out. It is the fourth of the six Light Up deductions, and you can try it on tonight's board.
Nightwatch is on Android. On iPhone, play tonight's board here.
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Questions
What is the best strategy for Sudoku?
Work by elimination. For each digit, find where it can still go in each box, row and column, and place it when only one square is left. Keep pencil marks up to date, and reach for pairs and pointing only when the singles run out.
What is an X-Wing in Sudoku?
An X-Wing is a pattern where one digit has exactly two possible squares in each of two rows, and those squares share the same two columns. The digit must sit on opposite corners of that rectangle, so it can be removed from every other square in those two columns.
What are pencil marks in Sudoku?
Pencil marks are small notes of the digits that are still possible in an empty square. They make patterns such as pairs, pointing and the X-Wing visible.
Is guessing allowed in Sudoku?
Nothing stops you, but a well-made Sudoku never needs it. Every step can be reached by logic, and a wrong guess can spoil the grid long after you made it.