Sudoku is a very addictive puzzle game that can be played virtually anywhere, and by anyone. The basic idea is to fill in a grid of 9x9 with numbers from 1 to 9 and never have the same number twice in any row, column or region. Sounds easy doesn't it. It is actually that easy... =)
I don't claim to be an expert in Sudoku, but I have solved 483 puzzles on my Palm PDA (I just counted them) and quite a few on paper and the Computer... So I would guess over 600 puzzles all in all... I have just snapped up thing from webpages and articles, I can't guarantee that everything here is correct, if you see something that is wrong please tell me. I'm doing my best to make it easy to understand, the whole idea seemed so alien to me when I first started playing with Sudokus...
Su Doku are two Japanese words and are pronounced sue dock-o, it means single number. It's a short for "suji wa dokushin ni kagiru" which means "the numbers must be single". Sudoku was invented by the American puzzle maker Howard Garns in the year 1979, under the name "Number Place", but it didn't get much recognition, even if it was published in Dell Magazine. In 1986 when it was introduced to Japan and given the name Sudoku it became popular, in 2005 Sudoku became a worldwide phenomena.
Table of contents:
The Board
The Basics
Pencil marks
Fish?
X-Wing
Swordfish
Jellyfish, Squirmbag and Gronk
The Board
This is the board, 81 fields to be filled, in a 9x9 square.
This is a called a row, this particular row is row 2 (R2, for short)
This is a column, column number 4 (C4)
This is a cell, in row 5 and column 4 (R5C4)
And finally this is a region, I like to number them from left to right and up to down so this would be region 2, (you could also say R1-3, C4-6)
The Basics
When you start a new game you will have some numbers filled in, so let's do that shall we.
This is how a game will look when you start it. Now remember that you can't have any one number in more then one place in any row, column or region.
Let's have a look at the 5's, you could start with any number but that just seems like a good example for now.
The only rule in this game states that no number can be more then ones in any row, column or region. That rules out all of this lighter areas. As you can see there are two cells that must be 5 (R1C8 and R8C3)
With those two cells filled in we get even fewer places where 5 can legally be, in the middle region it is one that is obvious since all another cells are either occupied or have a 5 in the same column (R5C4)
This is how far we get with the 5's for now, on to some other number, I guess you got the idea.
Pencil marks
Pencil marks are small numbers you write in the cells to remember which the possible candidates are.
This is our board with all the pencil marks filled in, as you can see there are several cells that have only one candidate, so here's how you make them:
Either you have a computer do it for you, that is the easy way to go, but if you are playing with pen and paper, or you feel like that is cheating, you will have to consider every number to be a possible candidate for every cell. So if we were to start at R1C1 you start by considering 1, that is already in the region so that is not a candidate, 2 is not in any row column or region though then write a small 2 in the cell. 3 is in the same row so that is not a legal candidate, 4 is though and so on... When you get to nine just go to the next cell and fill out the region like this.
When you get a cell that has only one candidate, you can safely erase all the pencil marks of that number in the row, column and area and make it into a "real" number.
You can solve entire easy sudoku puzzles like this one just by filling in pencil marks. in the example above the darker ones are single candidates and the lighter marked cells are single candidates after the darker ones have been removed. So with this logic you can get this far in only two steps.
This is called a hidden candidate.
Because cell number 5 and cell number 9 must be either 2 or 4, cell number 8 can't possibly be 4 and therefore has to be 7. This also happens in columns and regions.
This is a called a triplet.
the three numbers highlighted (4, 5 and 8) are has to be in those three cells, which means you safely can erase them from the other cells in the row (or column or region, if that's where you found it).
If you are with me this far you already know more then most people I know.. so let's go on... =)
Advanced Techniques - All those fishes
Fish?
I'm not sure what this is called but it happens all the time, it's like a fish pattern of the first order, if there is something like that...
anyway, because one of the two cells in the third region has to be 3 the one that are in the first region can't be three and can therefor be removed. All the lighter orange cells can be cleared of the number that makes up the pattern (3 in this example)
If you happen to know what this is called please tell me, it would be ice to know if it has a name.
The X-Wing
This is a X-Wing.
A x-wing occurs when there are two rows or columns that has only one possible candidate in two cells, in this example it's 6.
If we imagine that the top left one is 6 then then in the opposite corner (low right) also has to be 6, which means that both the rows and columns in the x-wing can't include the number 6.
This is the reason for the name X-wing.
These cells can't have a 6 in them, which means that we can remove a few pencil marks from the board without guessing. We can't remove the numbers in the corners of the x-wing itself though.
The Swordfish
This is a Swordfish, in this example it's the the number 6 that makes the pattern.
The Swordfish is much like a more complex X-Wing, you need three rows or columns with only two candidates. They also need to connect like in the picture, most often like a cube with a corner out of it. the important part is that you would be able to go around the pattern by turning 90 degrees at every corner.
There is actually two swordfishes made up of sixes on this board, can you see the other one?
As with X-wing you can't remove the pencil marks that are making up the actual Swordfish but everything that goes out from any or the edges. In this example there is only on candidate to remove (R2C4) but there are quite a big coverage.
This is how the pattern will look (like a box with a corner missing) I have't got a clue why it's called a sword-fish, doesn't look like one to me, there are also other variations of fish patterns so maybe there's some hidden logic there. I also found another one while fixing the image, the dark red cells.
The Sqirmbag (and Jellyfish and Gronk)
This is a "squirmbag"; it's a fish pattern of the 5'th order. Which means that there are 5 pairs of horizontal (or vertical) candidates... This is not a very good example because the odd candidate is sort of in the chain (R4C8) but they are so rare that when I stumbed upon one when playing last night I just had to take a snapshot...
The Fish patterns are:
X-Wing (2'nd order)
Swordfish (3'rd order)
Jellyfish (4'th order)
Squirmbag (5'th order)
Gronk (6'th -> infinite order)
I read that the Gronk pattern is not usable in 9x9 sized Sudokus, not sure why that is, probably it's too big.
As with all the other fish patterns you need to be able to go around it by turing 90 degrees at every candidate... like the image above.
The lighter square are what this little fish is covering, it's almost the whole board. The backside of this is just that you will most often have erased all eventual other cadidates before you notice the squirmbag. I had only one left, in this example.
More to come...