


The rules...

Sudoku has been built from a field of 9 large squares that has been subdivided by 9 small boxes. Therefor there are 81 boxes in total. In this field there are the numbers 1 till 9 placed randomly.
To start of easily we numbered the rows with the characters (A-1) and the columns with the numbers (1-9)
Now lets have a close look at a random and easy sudoku (pronounce soedokoe):
The intention is to put a number from 1 till 9 in each horizontal row (A-1), in such a way that each number will only appear in that row once. That isn't difficult. However, it's getting harder when that same number may also appear only once in the vertical column (1-9). And it's getting even harder when that same number may only appear once in the big cube of (3X3 boxes) where both the row and the column cross each other. That is the only task of a sudoko puzzle. No more and no less. A game that requires good observation, and common sence.
Try to solve the simple sudoko above with the help of the given instructions.
And here's an instant warning: only fill in a number after you're convinced that it will fit in the right position. You have to be absolutely sure that the number isn't showing on other places in the row, column or cube!! The position has to be unique…
The difficulty level of a sudoko puzzle is specified by the amount of numbers given at the beginning. It speaks for itself that the position of the numbers in the sudoko are of great importance, but you can't see them by forehand. Just to be absolutely sure: Sudoko has nothing to do with arithmatic, nor does it requires the knowledge of maths. The only thing you need is the ability to think logically. Guessing for the numbers you need is out of the question...
We are able to solve a sudoko by using several strategies.
Lets have a look at a few:
Method 1
On the top row (A) we see in the fifth space on the left (5th column) de number 4. In the third row (C) and in the 1st column we can also see the number 4. This means that both in row A and in row C no 4 may occur, and therefore the number 4 can only be placed in row B.
In every field we can place the numbers 1 till 9 only once as we have learned in the above.
In column 7 we see in cube 9 also a number 4. Because the space in column 8, row 4 is already taken, in our diagram by a 3, we can only put the number 4 in the right space (row B, column 9).
We fill in the number 4 and check in the vertical direction if there are any more options for this number:
There we see that we can place another 4 in row D in column 8, because this is the only free space and because there is also a number 4 in row F.

And so we keep looking if we can place the number 4 always in the 3 (big) cubes both in the horizontal and vertical direction.
Only with this method and with good observation is it possible to solve simple sukodo's. This method will be not be sufficient anymore when less numbers are given. And we have to look for more solutions.

Method 2
When we already put certain numbers in a puzzle, and there are 7 numbers in a row, column or cube, then there are only two spaces left to fill. Lets make this clear:
In row E we still have to place the numbers 2 and 8. Because we placed a number 2 in column 1 the only place left to put the 2 is therefore the 8th space in row E. The remaining 8 will be placed of course in the first space in row E.
We can see in column 4 that there are 3 spaces left to fill, namely the numbers 2, the 7 and the 9.
Number 2 is placed both in row A and C. Therefore we can only put the number 2 in space 2 of column 4. Because there is a 7 in row C, we can only put the 7 in space 1 of row A and the remaining 9 automatically goes to the last space (C4).
2 spaces to go in cube 2. Because the number 9 already appears in row B it will automatically go to row A, space 6 and the remaining 1 can only go to B6.

Method 3
We can also reach the next step by crossing off numbers. Lets have a look at cube 7 in the left corner. Here we already see the numbers 4, 9, 1, 2 and 7.
But we can still use this cube: we can see the number 3 appearing in column 3 and also in row 3. Lets use some help lines, and it occurs that in cube 7 the 3 can only be placed in space 1 of row 1.
We can only place a 3 in the spaces 8 and 9 of row H of cube 9. A 3 is now placed in the first space of row I. Since no 3 occurs in the columns 8 and 9 we keep these empty.
A different situation. We want to try to put the number 4 in cube 2. We see that both the numbers 2 and 6 occur in row A and column 4.
We crossed out the rows for you where the 4 occurs.
Since the numbers 2 and 6 can be placed in the indicated spaces we can put the number 4 in the remaining space.
Methode 4/5
Now we look at two possibilities in one diagram:

The above situation is important because there three numbers in a row which create a blockade.
An 8 in the above row (A) will be blocked in cube 1 row B. The only possibility for row C, space 1 or 3 is the number 8. Which leaves only one possibility for cube 2 namely in row B between space 4 or 6 (here the numbers 1 and 2).
In the part below we will have a look where we can put another number 4: the 4 appears in the columns 2, 5 and 7. This means that in cube 8 we can only place the number 4 in the bottom line namely in space 4 and 6. Line I is furthermore blocked for number 4. And because in row 8 the space 8 (here number 2) is already taken, it only leaves the space on the right side.
Method 6

Another much attended situation and with that the important help is the counting off of a row, column and cube. If there are eight numbers placed together, then the remaining one is easy to place.
In this example the number 6 is missing in cube 4. It can be only be placed in the crossing line of row E and column 3 since all remaining numbers (1-5 and 7-9) are present at least once in the indicated row, column and cube.

Method 7
Rest us only the method of crossing out numbers to localise the so-called 'single's, 'twins' and 'triplets'. Time consuming, but efficient. When it comes to very difficult to solve puzzles or when you think you're stuck, then here's a little tool to get you started again.


In here we assume that in every space of the entire puzzle the numbers 1 till 9 could appear. (81 spaces which could hold the numbers 1 till 9). As soon as one number is placed in one of the spaces, it will be clear that in a big amount of other spaces certain numbers have to be crossed out.
If a 2 will be placed in a random space, then all 'two's' in the concerning row, column and cube have to be crossed out. If next a 7 will be placed idem, etc. It speaks for itself that this time consuming. How can this help us?
Lets have a look at a single row with some of the numbers placed randomly:



If we could see the entire sudoku then it would occur that in the invisible part of the columns of column 2 all numbers are present with the exception of number 9. In column 4 all numbers with the exception of the numbers 1, 6, 9, in column 8 all numbers with the exception of the numbers 1, 5, 6 and 9 and in the final column all numbers with the exception of the numbers 6 and 9.
We will fill in the missing numbers in the row with small pencil figures. Now the row will look like this:



What we can do with this will be commented in the topic 'Singles'.
Singles
When after carefully placed or crossing out in a certain space of a row a single number occurs, then you can be 100% sure that this number can be put there. In English they speak about 'Singles'.

We can safely place the 9 (second to the left) in the above example and we can cross out the small 9 from the places 4, 8 and 9. There will be a 6 left in space 9 which we can place there for sure as well. Then there will be a single 1 left in space 4. Put it there…! Now look what's in the space left: the number 5.
And because of this we completed the row.
It could however well be that there is indeed the space to fill in a 'single', but that it is 'blocked' by other possible number candidates:

In the last space you can see a 5 as a 'single' in combination with some other options. Also here you can write the 5 safely down.
Situations like the ones beneath could also happen frequently:

In the cube on the far most right a 2 occurs in each bottom row. This means that in the remaining bottom row no 2 may/can be placed. Now in the top row, middle cube, a 'single' appears and we can safely put a 2 in space 3. Of course situations like these can also happen in 3 cubes underneath each other.

In the middle cube we can see the number 9 appear twice in the first column.
Because no 9 appears in the first row in both the above and below cubes,
there is no other way than that the 9 has to be placed in the middle cube in on one of the indicated places.
This means that the remaining nines in that cube may be crossed out or stuffed.
Normally we only use pencil marks in the spaces in a final stage of the puzzle so we don't have to waste any more time. Luckily we have some more possibilities to our arrangement with this time consuming crossing out method:

Twins
Are there in a row, column or cube twice the same two-figure numbers, with a minimum of three free spaces, then you can cross out these two numbers from the other spaces. The remaining number can now be placed. I will show it to you in the reversed order, in a random range, because I think this is the easiest way to understand it:


Now if we delete two numbers from this serie, then we will automatically see two figures which we recognise as 'Twins'. In these two spaces both a three and a six can be placed:


By filling in the small numbers in a diagram we can see, for example, the underneath number combination in which the two figured number combination 36 becomes a 'Twin'. We may now cross out the numbers from the 'Twins' with the remaining pencil notes from the diagram and we will see that we can fill in the 2 and the 7. We don't know yet where we can put the 3 and the 6 in this situation. These shall have to wait for a bit.


A different situation in which the 'Twin' is hidden:


Because in space four and five the numbers 1 and 9 appear and no where else in the row, we can exclusively put those numbers 1 and 9 in the mentioned spaces. The remaining figures in these spaces may be deleted and only one 'bold twin' will be left over.
Triplets
This is about a two two-figured letter combinations which, combined together, will make a new combination with the use of the same numbers. Or in other words: Only 3 different numbers may be used in 3 different spaces. For example: you have a row, column or cube which holds the figure combination 25 and 56. With this we can make the three-figure combination 256 (or the two-figure combination 26). Or with 14 (18) and 48 we'll get 148. In another order it is possible to make this a bit easier to understand: 37, 379 and 79, but 37, 379 and 39 also works. The third new figure combination doesn't necessarily have to exist out of three numbers. It can also exist of 2 numbers. But only if all three figure combinations are used with the same 3 numbers. For example: 36, 37 and 67 or 23, 24 and 34, etc. After crossing off you will find the figure combination in your diagram underneath. A 'Triplet' combination. With only three free spaces there is nothing you can do with it.


However, it is a different case if there are more free spaces available. For example, you have noted the following pencil-figure combinations:


By tracing the 'Triplet' 36 367 67 you can cross out these numbers from the remaining spaces and with that you may write down the numbers 2 and 1 in your puzzle. The 'triplet' itself has to wait till you have moved on in the puzzle.
And…, the 'Triplet' can also be hidden:


Together the numbers in the grey spaces form the 'triplet'. The remaining numbers can now be removed.
Quads
This is about four different numbers (in the example 2, 5, 7, and 9) which always appear in four different spaces. This means that these numbers may only appear in these four spaces, and with that they can be excluded from all other spaces. After crossing out you will see that the number 6 (which is now a 'single') is directly available for placing. What is left is a space 9 for number 8. After filling place 9 you can put number 1 in place 7 and 'last but not least' number 4 in place 6. Not long to go now…!


X-wing
A technique for the experienced....

To illustrate the importance, we left away all 'pencil marks' and we only focus on the number 6. You will find the number 6 on several positions in the diagram and also in the grey places 1 and 9. Lets have a closer look at these rows and we notice that number 6 appears both in space 6 and 9 of row 1 and 9. This means that when number 6 is finally placed in row 1 in space 6 the number 6 in row 9 can only be placed in space 9. (and vice versa) This pattern is called an X therefore the name X-wing…
When in a row a certain number appears only twice as a 'pencil mark' and those same numbers appear in a different row in the same spaces. Then an X-pattern is formed and all other equal 'pencil marks' from the concerning rows may be crossed out. This pattern is based on the columns. It also works reversed, but then based on rows…
More advanced solving techniques you can find at: Scanraid.com
Their Sudoku Solver you can find HERE
And finally
Those were some handy tips and hints which will help you to solve sudoku's. From easy till spicy. We wish you a lot of puzzle pleasure. If you have any addition to this sudoku-explanation we would appreciate it a lot if you would send it to us, so others could also make use of it. Thank you very much in advance for your trouble.
Our e-mail address: redactie@sudokusite.eu
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