#btw there is another simple technique called the Y-Wing because one star wars thing apparently wasn't enough

[capitalismwasamistake]

can tou give us fun facfs about sudoku plz i am interested

Anon, I am kissing you on the mouth

Here are five random sudoku fun facts!

(With detailed explanations for absolute beginners under the cut)

1.One of the most famous sudoku variants is called Killer Sudoku

2.Some sudokus have chess moves in them

3.The secret – the sum of the digits one to nine is 45

4.The sixteen digits in the 4x4 corners of a 9x9 sudoku are the same sixteen digits as the ring around the central box

5.One of the simple sudoku techniques is called the X-Wing (Sudoku Star Wars crossover? Not Clickbait??? 😱)

Explanations

First, a bit of notation. In sudoku, the grid is divided into rows, columns, boxes, and cells. Rows are named from top to bottom, and columns from left to right. Boxes are the 3x3 squares – they’re numbered left to right and top to bottom. The small individual squares are called cells. Cells are numbered by their row and column – roll one column three, roll four column seven, etc. You write R2C6 for short. Below you see a standard sudoku 9x9 grid with the rolls, columns and boxes labelled. The red cell is R1C3, the blue cell is R4C7, and the black cell is R2C6.

(Some people use lowercase letters in labelling cells, it’s a matter of personal preference.)

There are small digits in three cells in box 8. The centre digits in R7C6 indicate that this cell can only contain the digits one or two, but we don’t yet know which one – this gives us information about the individual cell only. The corner digits in R9C4 and R9C6 indicate that the digit three can only be in those two cells within the box – this gives us information about the box only, as each of those two individual cells may have other possible digits.

(This is a somewhat “standard” but by no means universal usage of centre and corner small digits)

With the jargon out of the way, let’s get into the neat sudoku details!

1.Killer sudoku

Funny name, right? Sounds dangerous!

Killer sudoku follows normal sudoku rules (the digits one to nine must be placed once each in every roll, column, and box of the grid), but adds “killer cages” – groups of cells outlined in a striped line. At the corner of the killer cage you can see a number, which represents the sum of the cells within the cage. Digits cannot repeat in a killer cage.

This doesn’t seem like a lot, but it actually gives you plenty of information – like in the example below, where you see R5C5 and R5C6 in a cage whose total is 17 – there is only one way to make two cells add up to 17 in sudoku, and that is 8+9=17. Therefore you now know that those two cells contain the digits eight and nine in some order.

With killer cages it’s easy to make a grid that doesn’t have a single given digit yet still has a unique solution!

2.Chess constraints

Another popular subsection of sudoku variants is the so-called chess move constraints. The most popular is the knight’s move constraint – a sudoku having a knight’s move constraint means that, if you imagine the grid as a chess board, no digit can be placed within a knight’s move from itself. In the below example, the digit in the red cell (R5C5) cannot be placed in any of the blue cells under a knight’s move constraint.

The other two chess move constraints are the king’s move – a digit may not be placed in any of the surrounding eight cells; and the queen’s move constraint.

Bonus mini fun fact! Queen’s move constraints are used sparingly in sudoku, and for good reason – when you see them, they’re usually applied only to a single cell in the grid. That is because you cannot build a sudoku grid where every cell and digit is subjected to the constraint – try it yourself! Open Sudoku Setter and you’ll see that you can’t even make a single digit satisfy this constraint. Knight and king’s move’s constraints are much more forgiving, and you could build a sudoku that satisfies them relatively easily.

3.The Secret

That one’s easy: 1+2+3+4+5+6+7+8+9=45

But why do you need to know it? Well, the Secret can help you in a lot of sum-based sudoku variants, such as killer, sandwich, or skyscraper. It can also help with geometry-based sudokus that use sudoku set theory, but that’s a topic for another day.

In the bellow example, which uses killer cages, you can see that one of the cages in box 4 extends by one cell into box 1. You know the total of the box (45), and you know the total of all four cages – 50. You know, therefore, that the single extra cell in box 1 must account for the difference between the box total and the cages total. So now you know that R3C3 is exactly 5!

Bonus mini fun fact! We call it “the secret” after two prominent figures in the sudoku community – the hosts of the YouTube channel Cracking the Cryptic, Simon Anthony and Mark Goodliffe. The two of them started calling it that a while back and it caught on. I greatly recommend their channel if you want to learn more about sudoku – they post two sudoku solving videos every single day and allow you to use their very comfortable solving software Sudoku Pad to try to solve the puzzles along with them! They got me into variant sudoku in the first place and I cannot sing them enough praises!

4.The Phistomefel ring

Another geometry-based sudoku technique, the Phistomefel ring is named after the sudoku setter Phistomefel, who first used it. It says that the four digits in each of the grid corners (highlighted in yellow bellow) correspond to the sixteen digits around the central box (highlighted in blue). This is true for all 9x9 grids that abide by normal classical sudoku rules! Isn’t that neat?

Here's Simon from Cracking the Cryptic giving a simple geometry explanation for why that is!

This technique comes up in sudokus with medium to high difficulty and it’s a bit situational, but can really crack open a puzzle. I included it mostly because it’s a cool property of sudoku grids!

5.The X-Wing

Let’s end it all by highlighting that we’re actually massive nerds. The X-Wing is one of the easiest to learn sudoku techniques. It’s easiest to illustrate with an example, so look at the image below:

The situation is this: the two cells in box 4 are a one-two pair – meaning that those two cells contain the digits one and two in some order. In box 6, the two digits are a one-eight pair – they contain the digits one and eight in some order. You’ll notice that those two pairs share rolls – both are in rows four and five. And both of them contain the digit 1. Classic sudoku rules tell us that the digit 1 must appear once in row 4, and once in row 5. The pairs each have a one, therefore they account for two instances of the digit 1.

So two situations are possible now. Option one: R4C3 is a one – in which case R4C8 can no longer be a one and will be an eight – and therefore R5C8 is also a one. This is the “yellow” state of affairs, as per out highlighting. Option two: R5C3 is a one – in which case R5C8 can no longer be a one and will be an eight – and therefore R4C8 is also a one. This is the “green” state of affairs.” In either state of affairs, the instances of the digit 1 in rolls 4 and 5 are accounted for by the two pairs.

You may notice that the “yellow” and “green” options cross – forming something like an X shape, which some nerd decided reminded them of the X-Wing ship from Star Wars. So we now say that those two pairs form an X-Wing of the digit 1.

Why is an X-wing useful? Look at the central cell, R5C5 – at some point we’ve deduced that it can only either be a one or a four. Now look back at the X-Wing: it only gives us two sets of affairs: “yellow” and “green”. What happens if we have the “yellow” state of affairs? R5C8 is a one, meaning that R5C5 cannot be a one and must be a four. Switch to the “green” state of affairs: R5C3 is a 1, meaning that R5C5 cannot be a 1 and must be a 4. Conclusion: the X-Wing tells us that R5C5 is always a 4! It gives us a digit for free!

This is true for all cells within the X-Wing – once you have it, you can remove 1 as an option from all the cells between R4C4 and R4C7, as well as between R5C4 and R5C7!

Anon, I’m sorry, or maybe you’re welcome.

All example images created with F-Puzzles Sudoku Setter.