How to Solve Sudoku Manually
Here you can finde some general hints on how to solve a Sudoku manually with pen and paper.
topMarks
Many authors recommend to mark cells in the following way: For each number that may be entered in a cell make a tick mark at a different position inside the cell. If you enter a new number somewhere, you have to rub out all ticks that don't make sense any more. See the Wikipedia for reference.
This method can be useful, but it is a lot of work which is often superfluous. Additionally it is easy to draw a tick to long so that it accidentally marks a neighbor cell. Clean rub out is not always easy as well.
But most important: With this method you can only remember what numbers can be in a cell, but not where a number has to be inside an entity, let's say inside a 3x3 block.
I suggest to note where a number has to be within a 3x3 block.
A little example illustrates how useful this can be:
 An example Sudoku
We will try to find a place for a 3
in this Sudoku. At
first glance that doesn't seem to be easy.
We chose a few blocks and mark where the 3
has to
be:

In a few blocks the cells where marked where a
3
has to be.
If you look at the upper middle 3x3 block you can see that all marks
are in the same row. Now we know that in the rest of this row there
can't be a 3
.

In the upper middle block the
3
has to be in the first row.
Applying this knowledge to the upper right
block helps us to place a 3
:

In the upper right block we can place a
3
.
If we apply the same logic to the middle block, we can place the
3
in the upper middle block:

In the middle block the
3
has to be in left column. That helps us to place a3
in the block above.
When searching for nearly full entities the markings described first are still useful.
Therefor I recommend to use both kind of markings, for example noting the numbers that can go into a cell in the upper half and the markings that show where a number has to be in the lower half.
I'm Stuck. What Should I Do?
If you used all the techniques described here and you are still stuck, then I recommend to make a pause. After half an hour it will look much less difficult.
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