Strategies



Basic tests

The basic rules are two, the easiest and the ones that anyone can dicover just by scanning rows and columns and thinking a little bit.

Basic Test 1.-
Check in one cell if only one number can be writen without any conflict with the other numbers in the row, column or 3x3 group.
Basic Test 1 example.
Basic Test 1. The red '4' is the only number we can put in that cell, any other would conflict with the numbers in the row, column or 3x3 group.
You can apply this test to all cells in the board.

Basic Test 2.-
Check in one row, column or 3x3 group if one numbers can be put only in one cell.
Basic Test 2 example.

Basic Test 2. In the third row the red '8' can be placed only in the third cell because in the other two empty cells it would conflict with other '8'.
You can apply this test to all rows, columns and groups of 3x3 cells.
Both basic tests can be repeated every time that one cell filled, but not when a posible number is removed (see later).
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Small Numbers

From now on what we need is to mark or write down all posible numbers for each cell. The best way is to use small numbers written in the cells and remove them one by one when we find a rule that demostrate that certain number can not be placed there.
Small Numbers.

After clicking CONTROL+ALT+SHIFT + mouse click all small candidate numbers are filled. And when we put the number '9' in the last row, one cell changes to red, because the small '9' should be removed.
To write all that small numbers can be long and tedious, and is easy to make mistakes, but FreeSudoku can help a lot. With doble-click on a cell you can enter small numbers, only the posible ones. And when you fill other cells and some small numbers become inconsistent, the cell color switchs to red to show you that you should remove one candidate.

But that's not all, if you press the CONTROL key and then click on a cell, in the message area below you will see all posible candidates for that cell.
And if you are lazy enougth you can even press CONTROL-SHIFT + mouse click and the posible numbers will be authomatically written down in the cell.

And for people so lazy as me there is still another tricky; pressing CONTROL+ALT+SHIFT + mouse click on any empty cell ALL remaining cells will be filled with all posible numbers!

This way you can concentrate on thinking in the next tests and rules instead of writing minuscule numbers and trying to remove them without becoming crazy.
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Intersections

With this test we can check all intersections of a row or column with a 3x3 box. If we find that one number is only posible in the intersection for one unit (any row/column or 3x3 box) then we can remove that number from the rest of the other unit that intersects, because we know that that number is for sure in the intersection and can not be twice.
Intersection example.
Example 1
The numbers with the red dot can be removed because they are in the intersection with the box, and in no other place of the box.
Maybe it is easier to explain with examples:

If you look at the blue 3x3 box in the Example 1, the number '4' appears only in the first row (the ones with the green dot) that is also the intersection with the first row of the board.
So we now that the number '4' has to be in the first arrow of the blue square, and we can conclude that it can not be in any other cell of the first arrow of the board, so we can safely remove the numbers '4' with the red dot.
After removing the two numbers with the red dot we can easily complete left square and remove a lot more candidate numbers in other cells of the board.
Intersection example.
Example 2
In this case we can remove the numbers '8' with the red dot from the bottom box.


In the Example 2 we can see a similar case, but this time we can remove the numbers '8' with the red dot of the bottom box, because in the rigth column of this board the number '8' appears only in the intersection (green dots) with box.
After this we will be able to complete the cell with the number '2' and to remove some other small numbers.

We can use this test with all kind of intersections of three cell, and remove small numbers either in the box or in the row/column. We can distinguis four diferent types of intersections:

1.-Box with row -> Remove candidates from row (example 1).
2.-Box with row -> Remove candidates from box.
3.-Box with column -> Remove candidates from column.
4.-Box with column -> Remove candidates from box (example 2).

This test is not difficult to apply and is very helpful because usually we can remove a lot of candidates if we are lucky.

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Naked Pairs

This technique consist in finding two of cells in the same unit (any row/column or 3x3 box) with the same pair of numbers in both. Then we can safely remove all occurences of that two numbers in the rest of the cells of the unit (I'm always talking about the small candidate numbers in the cells).
Naked Pairs example.
Example 3
In the last row we have found the Naked Pairs (with green dots), so we can remove the numbers with the red dots.


Let's check Example 3: In two cells of the last row we can find the pair 4-7, the ones with the green dot. This pair is twice in the row and there are no other numbers in that cells, so we have found a Naked Pair!
We can remove all the numbers 4 or 7 of all the other cells of the row, only of the row in this case, the ones with the red dot.

Why? because we know that the numbers 4 and 7 are in those two cells, the 4 in one cell and the 7 in the other one. We don't know which number goes to each cell but for sure that both are in that two cells, so they can not be in any other cell of the group. But be careful, they can be in other cells of the 3x3 boxes, we should remove them only from the unit where the pairs are, in this case the row.
Naked Pairs example.
Example 4
Here the Naked Pairs are in the left 3x3 box. We can remove also the numbers with the red dots.

Following with the same example, after filling one cell and removing some other small numbers, if we check again we can identify another pair, but this time in the left 3x3 box (example 4), the pair 2-6 is twice!
So we can remove the other numbers 2 and 6 of the box, the ones with the red dot. And if you want to do the exercise, you can continue with another naked pair.
We could also have seen a naked triple in the rigth box, but this come later!
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Hidden Pairs

Hidden pairs are little bit more complicated and harder to find. Is the inverse principle of the Naked Pairs, now we have to find two pairs of numbers that are in two cells but mixed with other numbers. The condition now is that numbers can't appear in any other cell of the group, even separate. In such a case we can eliminate all other numbers that are together with the pairs, in the same cells.
Hidden Pairs example.
Example 5
The 7 and 8 are the Hidden Pairs, so we can remove the numbers with the red dot.


In the Example 5 we can see that the numbers 7 and 8 are only in two cells, so we can remove the other numbers in that cells, because both numbers have to be in that two cells, there is no other place, so the other numbers can not be placed also there.
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Naked Triples

Coming soon...
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Hidden Triples

Coming soon...
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