Q. What sport uses balls weighing 2.7g with a diameter of 40mm?

# How to Solve Sudoku Puzzles

## Learn How to Solve Sudoku Faster!

To get better, learning the different solving techniques will certainly help. However, in the real world, when you don't know which techniques you'll need, spotting them becomes the challenge even if you know them! The best way to get better at spotting them is by practicing to find those hidden techniques, starting with the ones you find easier and slowly building up your experience.

You can play online sudoku on this site. All the puzzles are graded by the relative difficulty of the hardest technique required to solve them and include a wide range of techniques for you practice.

Or we recommend you try 300 Sudoku Puzzles: Easy to Extreme which starts you off with very easy puzzles, requiring singles only, and gradually introduces a very wide range of increasingly difficult techniques, all the way up to forcing chains at the extreme end! By using this site or book, with a guide to learn the techniques, you will get better and faster at spotting them and become a sudoku master in no time!

### The Sudoku Puzzle

Sudoku puzzles are very simple in concept (and good for the brain!) - you fill in a 9x9 grid with the numbers 1 to 9 making sure no number is repeated in any row, column or box - however the logic behind them can become very complex! Some puzzles are very simple, yet others are seemingly impossible even though they can be solved using logic, without the need for guessing or trial and error.

On these pages we are developing a series that looks at basic solving techniques needed for every puzzle and explanations of the more advanced methods needed to solve more difficult puzzles.

There are many variations of sudoku puzzles available now including 16x16 grids, Sudoku-X and Killer Sudoku. We will be concentrating on the original 9x9 sudoku variant but many of the techniques will still be applicable.

A 9x9 sudoku puzzle will typically:

• Have only one, unique solution
• Have 32 or less "givens"
• Have at least one element of rotational or reflectional symmetry
• Be solvable using only logic

Having a unique solution, solvable by logic, is a must to be fair to the solver. The other two are matters of editorial standards.

Generally the more givens there are the easier a sudoku puzzle is, but it is possible to create puzzles with far more givens than 32 which are extremely difficult to solve. Symmetry is mainly a matter of aesthetics and doesn't change how easy or hard a sudoku puzzle is - as soon as you've filled in a number or two the symmetry is usually lost! The tradition established by Nikoli (the creator of Sudoku as we know it!) is to use 180° rotational symmetry but horizontal, vertical and diagonal reflectional symmetry can offer a visually pleasing deviation from the norm and isn't unusual to find. Non-symmetrical grids are perfectly valid puzzles, but symmetrical ones "looks nicer"!

Conversely, the opposite tends to be true and fewer givens means it's likely to be harder, but it shouldn't be used as a guide to how difficult a sudoku puzzle is as it's possible to create a very easy sudoku with the minimum 17 givens possible which requires only the very basic technqiues to solve!

And finally, while computers are so fast they can use brute force to solve a sudoku puzzle in the blink of an eye by trying every combination until they find the answer, humans don't enjoy guessing randomly until they stumble upon the solution!

## How to Solve Easy Sudoku Puzzles

### Basic solving techniques

Every sudoku puzzle, no matter how hard, is reduced through elimination to basic "singles" so they are an absolute must to know to solve any sudoku! Easy puzzles can usually be solved using only "singles" and are great for beginners to practice finding singles.

The simplest of these is the Full House where there is only one number remaining to input in the row, column or box. The other eight numbers are known, so there is only one possibility for that remaining cell and is the easiest to spot.

A Naked Single is where there is only one possible candidate (option) for a cell as it already intersects with 8 different numbers within the same row, column and box.

A Hidden Single is where there may be many candidates for a particular cell, but it is the only position in that row, column or box where a particular number can go.

If you are playing with candidates (writing in all possible options left for each cell before solving), then the naked single will be far easier to spot. If you are playing without entering candidates, which is often unnecessary and quicker for easy puzzles, then the hidden single will be easier to spot.

As we develop this guide, you we will introduce you to different techniques to spot this such as "scanning" or "cross-hatching" to help you find the singles.

## How to Solve Medium, Hard or Difficult Sudoku Puzzles

### Moderate and Advanced solving techniques

As you progress to more difficult sudoku puzzles, you will generally need to use candidates, except for the "direct" techniques. As we develop this sudoku guide we will explain different techniques and how to spot them, plus tricks, hints and tips to help you solve them. There is a "formula" you can use to solve almost every sudoku, but the hard part is knowing what to look for!

There is no real "trick" to solving hard sudoku puzzles, it comes down to knowing how to logically apply a series of steps to mathematically reduce a puzzle to the point where it becomes solvable by hidden and naked singles alone through a process of elimination of candidates.

These are some of these are some of the techniques on our list to add to our guide as we develop it. The difficulty levels are not an exact science as one person may find spotting a Jellyfish much easier than an X-Wing, or compared to someone else they have a blind spot for Skyscrapers! Everyone finds certain techniques easier or difficult than others might, but they are presented here in a rough order of how difficult people find them. It also depends on the puzzle itself or how many candidates are left, and some techniques could be thought of as overlapping difficulty boundaries depending on the circumstances. There are often multiple paths that can be used to solve a sudoku puzzle, including far more advanced techniques than necessary, and they can lead to a shorter solution path if you are good at spotting them. If you want to use a Kraken Fish to solve an easy puzzle you can, but it's a bit overkill!

### Moderate Sudoku Techniques

The "direct" methods listed below are essentially the same as their general counterparts later on, but the key difference is that they reveal a hidden single immediately by eliminating key candidates. It is possible to find them without writing in candidates as you don't need to keep track of eliminations and can directly fill in a number, subsequently forgetting any other eliminations the technique might have given you. This makes them a special case and a kind of hybrid of a hidden single with intersections or pairs and triples.

Direct Hidden Triple

From here onwards though, you will need to keep track of candidates to either spot a method or keep tabs on any eliminations for later reference. If you are a sudoku master (or have an eidetic memory!) then maybe you can solve advanced puzzles without using pencilmarks through very advanced techniques such as "trailing" and "uniqueness". These make use of the fact that a sudoku puzzle has (or should have!) a single solution, and by forming often lengthy chains of logic in your mind it is possible to test if a certain placement of a number can be true or not, potentially revealing shortcuts to solving the puzzle. It's best to have a thorough understanding of all the methods and concepts by using candidates first though!

Pointing
Claiming
Locked Pairs
Hidden Pairs
Naked Pairs

Locked Triples
Naked Triples
Hidden Triples
X-Wing
Swordfish
Simple Colouring
Skyscraper
2-String Kite
Turbot Fish
XY-Wing
Finned X-Wing
Remote Pair
XYZ-Wing
W-Wing
Empty Rectangle
Uniqueness Tests

### Fiendish Sudoku Techniques

Bivalue Universal Grave (BUG)
Jellyfish
Sashimi X-Wing
Multi-colouring
X-Chain
XY-Chain
Nice Loop / Alternating Inference Chain (AIC)
Almost Locked Pair
WXYZ-Wing
Sue de Coq
Finned Swordfish
Squirmbag
Whale
Leviathan
Death Blossom
Almost Locked Triple
Fraken Fish

### Extreme Sudoku Techniques

Bivalue Universal Grave (BUG)
Mutant Fish
Sashimi X-Wing
X-Chain
XY-Chain
Almost Locked Pair
WXYZ-Wing
Sue de Coq
Finned Swordfish
Kraken Fish
Forcing Chain
Forcing Net

Play online sudoku now or check out our 300 Sudoku Puzzles: Easy to Extreme book!

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