# List of Sudoku Solving Techniques Worth Mastering

Solving Sudoku puzzles requires the use of various techniques.

How advanced the techniques you’ll need to use to crack Sudoku puzzles depends on how difficult the puzzles are. That’s one of the great things about Sudoku – you can start mastering the simpler techniques and then move on to more advanced Sudoku puzzles.

But to achieve this, you first need to know what the solving techniques are. So this article will list, in roughly increasing complexity, all the different techniques you should be aware of.

For each technique, we’ll give a brief overview of the process behind it. For the more popular ones, you’ll also link to resources where you can learn more about them.

## Simple Sudoku solving techniques

Let’s start off with some simpler techniques that you can use to solve beginner puzzles.

### Pencil marking

This is the most basic and common technique.

Pencil marking involves writing small numbers to represent possible candidates in empty cells. If you’re solving online or on a phone or tablet, the app or website you’re using will most likely let you pencil mark digits in as well.

This method can identify when only a single number can fit in a particular cell (known as a single), and also help with the hidden and naked strategies listed below.

You can learn more about solving Sudoku puzzles with pencil marking here.

### Hidden pairs

This is the first of many techniques that relies on proper pencil marking.

A hidden pair is when you have the same two digits pencil marked in precisely two cells within the same row, column, or 3×3 block.

What makes them ‘hidden’ is that there is at least one other digit also pencil marked in at least one of these cells.

Consider the hidden pair example below.

Because the digits 1 and 7 only appear in the last two empty cells, you can immediately remove the 8 and 6 as candidates.

To know why, check out our article on hidden pairs here.

### Hidden triples

Very similar to hidden pairs, except there are three, not two, digits that only appear in three cells within the same row, column, or 3×3 block. Such as in the example below.

To explore this solving technique in more detail, check out our guide on hidden triples here.

### Naked pairs

You can think of a naked pair as the inverse of a hidden pair.

Instead of having two digits that only appear in two cells within the same area, you have two cells with exactly the same two digits as the only candidates. Such as in the example below.

In this example, you can immediately remove the 1 and 7 as candidates in the top left cell, letting you write in the digit 3 to the grid.

To understand why, check out our guide on naked pairs here.

### Naked triples

The relationship between naked triples and naked pairs is the same as the relationship between hidden triples and hidden pairs.

That is, you have the same three digits as the only candidates in three cells within the same area (row, column, or 3×3 block). Such as in the example below.

Having identified this, you can resolve every digit within this 3×3 block. For a step-by-step guide to this process, check out our guide on naked triples here.

## Advanced Sudoku techniques

Let’s step things up a notch and tackle some more advanced solving techniques.

### X-Wings

An X-Wing is a particular pattern formed by pencil marks within four cells in the grid that line up across two different rows and columns. Thereby forming an ‘X’ pattern such as in the example below.

By identifying this pattern, you’re potentially able to eliminate other pencil markings elsewhere in the grid.

To learn more about the pattern, how to spot it, and how the technique can help with solving Sudoku puzzles, check out our guide on X-Wings here.

### Y-Wings

Looking for Y-Wings is a similar strategy to looking for X-Wings. However, the pattern you’re looking for only involves three specific cells, which makes it appear like a ‘Y’ instead of an ‘X’.

While the fundamentals underpinning the solving technique are the same, check out our guide on Y-Wings to learn how to spot the pattern and how it can eliminate candidates.

### The Swordfish technique

The Swordfish is an advanced technique that essentially takes the concept of X- and Y-Wings to a new level.

Instead of just looking for three or four cells containing the same pencil marked digit, Swordfish involve a 3×3 nine-cell pattern. Such as in the example below.

Learn more about the Swordfish technique here.

### Phistomefel Ring

The Phistomefel Ring is a particular pattern where the exact digits that form a ‘ring’ around the central 3×3 block must appear in the 16 cells that form the four 2×2 corners of the grid.

This pattern is shown below.

Knowing that this pattern exists can help you resolve and potentially remove candidates from these regions.

### The Rule of 45

Forty-five is a special number in Sudoku as it’s the sum of the digits 1-9. Therefore, in a solved Sudoku puzzle, each row, column, and 3×3 block will sum to 45.

Where knowing the Rule of 45 becomes helpful with solving puzzles is when you’re playing variants such as Killer Sudoku or Sandwich Sudoku.

## Extreme solving techniques

The list of advanced Sudoku techniques only gets more and more complex from this point.

The following techniques and strategies really only come into play when solving the most truly challenging Sudoku puzzles.

- X-Cycles
- XY-Chain
- 3D Medusa
- Jellyfish
- Unique Rectangles
- Fireworks
- SK Loops
- Extended Unique Rectangle
- Hidden Unique Rectangles
- WXYZ Wing
- Aligned Pair Exclusion
- Exocet
- Grouped X-Cycles
- Empty Rectangles
- Finned X-Wing
- Finned Swordfish
- Alternative Inference Chains
- Digit Forcing Chains
- Nishio Forcing Chains
- Cell Forcing Chains
- Unit Forcing Chains
- Quad Forcing Chains
- Almost Locked Sets