Skip to content
PuzzleTemple

Sudoku techniques step by step: from singles to X-Wing

Updated

Every Sudoku level you can play on Puzzle Temple is solved with the same short list of techniques. A technique is just a pattern that proves something: that a digit belongs in a square, or that a digit cannot be in one. This guide goes through the ones you will meet, from the simplest to X-Wing, and says which levels need which. If you are new to the game, start with how to play Sudoku.

Candidates: the idea behind everything

A candidate is a digit a square could still be. At the start, an empty square has up to nine candidates, and every digit placed in its row, column or box removes one. Almost every technique below either finds a square that is down to one candidate, or finds a reason to remove a candidate from some squares. You can keep candidates in your head, but writing them down as notes makes the patterns far easier to see.

1. Scanning

Pick a digit and look for where it can still go. Each copy of that digit already on the grid rules out its row, its column and its box. Do this for all three kinds of group and you will often find a box, row or column where only one square is left for the digit. Scan digit by digit, starting with the ones that appear most often. It needs no notes at all.

2. Naked single

If the digits already placed in a square's row, column and box add up to eight of the nine different digits, the square has only one candidate left, so that is its digit. It is called "naked" because the single candidate is in plain sight in the square itself.

3. Hidden single

The reverse view: look at a group (a row, a column or a box) and ask where one particular digit can go. If it fits in only one square of that group, it goes there, even if that square still lists other candidates as well. It is "hidden" because the square looks undecided until you ask about the digit instead of the square.

In this box only the centre square can be a 6, so it is a 6, although it also lists 2 and 9.

Naked and hidden singles are all you need for Easy, Medium and Hard. Those three levels differ in how many clues you start with, not in the techniques they use.

4. Naked pair

If two squares in the same group each have exactly the same two candidates, say 3 and 7, then between them they must hold a 3 and a 7. No other square in that group can be a 3 or a 7, so you can remove both digits from every other square in the group. The squares do not have to be next to each other; they only have to share a row, a column or a box.

The two outlined squares are a 3-and-7 pair. In the shaded squares the 3 and the 7 are crossed out, because they can go.

5. Locked candidates

Two patterns, both about a digit that is "locked" into a line inside a box:

  • Pointing. In a box, if every square that can hold a certain digit lies in one row (or column), the digit has to be in that row inside this box. So it cannot be anywhere else in that row, outside the box.
  • Claiming. The same idea from the other side: in a row or column, if every square that can hold a digit lies inside one box, the digit has to be in that box's part of the line. So it cannot be in the other squares of that box.
In the top-left box a 5 can only go in row 2 (outlined), so the 5s elsewhere in row 2 (crossed out) can be removed.

Locked candidates, together with naked pairs, are what an Expert puzzle asks for: it cannot be finished with singles alone, but it does not need anything harder than these.

6. X-Wing

Pick a digit, say 4. Find two rows in which the 4 can go in only two squares each, and those squares lie in the same two columns. Together they form the corners of a rectangle. In a finished grid the 4 in those two rows has to sit at opposite corners: either top left and bottom right, or top right and bottom left. Either way, each of the two columns gets its 4 from these rows, so no other square in those two columns can be a 4. The same pattern works with rows and columns swapped.

The 4 in rows 2 and 6 can only be in columns 3 or 7 (outlined). Other 4s in those columns (crossed out) can be removed.

X-Wing is one of the usual next tools when singles, pairs and locked candidates have run out. Extreme puzzles on Puzzle Temple are the ones that are still stuck after those, so they ask for techniques of this kind.

Which levels need what

LevelTechniques it needs
Easy, Medium, HardNaked and hidden singles
ExpertLocked candidates or naked pairs, as well as singles
ExtremeBeyond those; X-Wing is a typical next tool

A routine that works

  1. Scan for singles until the grid stops giving you any.
  2. Fill in notes for the squares around the part of the grid that is stuck.
  3. Look for naked pairs in each row, column and box.
  4. Look for locked candidates: a digit that is confined to one line of a box, or one box of a line.
  5. Only then look for wings like X-Wing. After any elimination, go back to step 1: a new single often appears.

Ready to try it?

Play Sudoku