# Sudoku Techniques: Singles, Pairs, Pointing and X-Wing Explained

Source: https://silverapuzzles.com/guides/sudoku-techniques

Sudoku techniques fall into three tiers. Singles (naked and hidden) place digits directly. Intermediate techniques such as pointing, claiming and pairs remove candidates so that new singles appear. Advanced patterns such as the X-Wing do the same across several rows and columns at once.

## How the tiers map to our difficulty levels

Every sudoku on Silvera PuzzleClub is graded by a program that solves it the way a person would, using the techniques below in order. If singles are enough, the grid is **Easy** (36 or more givens) or **Medium** (about 30 givens). If it also needs pointing, claiming or pairs, it is **Hard**. If those still stall, it is **Expert**. All the examples below use pencil marks: small candidate digits in each empty cell.

## Naked single

A cell has only one candidate left after removing every digit that appears among its peers. That candidate must be the answer for the cell.

*Figure: The middle cell has only one candidate, 7, so it is a 7.*

## Hidden single

A digit can go in only one cell of a row, column or box, even if that cell has other candidates. The digit must go there. Hidden singles are usually easier to find by scanning than by reading pencil marks.

*Figure: In this box the candidate 4 appears only in the center cell, so the center is 4 even though 1 and 8 are also listed there.*

## Pointing (locked candidates)

If, inside one box, all the candidates for a digit lie in a single row (or column), that digit must be in that row within this box. It can therefore be removed from the same row in the other two boxes. This is called **pointing**, because the box “points” along the row.

*Figure: In the left box, 7 can only be in the middle row. So 7 can be crossed out of the middle row in the other two boxes.*

## Claiming (box-line reduction)

Claiming is pointing in reverse. If, inside a row (or column), all the candidates for a digit fall within one box, that digit must sit in that part of the box. It can be removed from every other cell of that box.

For example, if the only places for a 2 in row 7 are two cells in the bottom-left box, then the 2 for that box is in row 7, and any 2s pencilled in rows 8 and 9 of that box can be erased.

## Naked pair

Two cells in the same unit that both have exactly the same two candidates, say {3, 8}, must hold those two digits between them. No other cell in that unit can be 3 or 8, so you can cross those candidates out everywhere else in the unit. The same idea works for three cells sharing three candidates (a naked triple).

*Figure: The two shaded cells can only be 3 or 8, so 3 and 8 can be removed from the rest of the row.*

## Hidden pair

If two digits each appear as candidates in only the same two cells of a unit, those two cells must contain those two digits. Any other candidates in those two cells can be erased. Hidden pairs are harder to spot than naked pairs because the extra candidates disguise them.

*Figure: 4 and 6 appear only in the two shaded cells, so those cells are 4 and 6 and their other candidates go.*

## X-Wing

The X-Wing is the first advanced pattern most solvers learn. Pick a digit. If in two different rows that digit has exactly two candidate cells, and those cells line up in the same two columns, the four cells form a rectangle. Whatever happens, the digit occupies two opposite corners of that rectangle, one in each of the two columns. So it can be removed from every other cell in those two columns.

*Figure: In the first and fourth rows shown, 4 fits only in the second and seventh columns. Those four cells form an X-Wing, so 4 is removed from the rest of both columns.*

The same pattern works with columns and rows swapped. Larger versions with three or four rows are called Swordfish and Jellyfish.

## When you are stuck

1. Make sure every cell has complete, up-to-date pencil marks.

2. Sweep each unit for hidden singles again; one new digit often unlocks several more.

3. Look for pairs, then pointing and claiming, unit by unit.

4. For expert grids, check each digit for an X-Wing.

Practice: [today’s daily sudoku](https://silverapuzzles.com/sudoku/daily) · [easy](https://silverapuzzles.com/sudoku/easy) · [medium](https://silverapuzzles.com/sudoku/medium) · [hard](https://silverapuzzles.com/sudoku/hard) · [expert](https://silverapuzzles.com/sudoku/ultra-hard)

## Frequently asked questions

**What is the difference between a naked single and a hidden single?**
A naked single is a cell with only one possible digit. A hidden single is a digit with only one possible cell in a row, column or box, even if that cell has other candidates.

**What is a pointing pair in sudoku?**
When all candidates for a digit inside a box lie in one row or column, the digit can be removed from that row or column outside the box.

**When do I need an X-Wing?**
Only in harder puzzles. On Silvera PuzzleClub, Easy and Medium need singles only, Hard needs pairs or pointing, and Expert puzzles are the ones where advanced patterns such as the X-Wing come in.