There are a number of strategies for solving Sudoku, ranging from the very simple to ones that might make your brain overheat a bit. The simpler puzzles can often be solved using only the simpler problem solving techniques. For the hardest puzzles you'll have to use them all. We'll cover them one by one - first of all, "line drawing".

(I should mention here that there don't seem to be standard names for the different techniques, but we have to call them something - so "line drawing" it is.)

__Line Drawing:__ this is the most straightforward technique, and the easiest one to use if you're solving a sudoku on the train on your way to work. It doesn't involve lots of counting and marking, and it can often solve quite a bit of the puzzle.

Let's look at this board and think about where we could place a 5 in the upper left box.

The second row also already contains a 5, at position [9,2], so we can mark all of the second row in green as well.

Finally, we have 5 near the lower left hand corner, in position [2,7], so we can mark all of its column in green.

Now that we've marked these areas of the board we can have a look at the 3*3 box at the upper left, and note that of the 9 squares, we've marked 7 as being unable to contain a 5. Of the other two squares, one of them [1,3] already contains the number 1, which leaves us with just one square [3,3] which could contain the 5. Since every 3*3 box must contain a 5, this square must contain a 5 - and we've solved our first square of the puzzle.

Now a couple of pretty obvious things, but I'll say them anyway:

- once you've solved a square, you may have opened up a number of other possibilities, so it's worth looking over the puzzle again, including all of the bits where you didn't find a solution the last time.
- the puzzle would quickly become unreadable if you drew lines all over it, so you'll mostly be tracing the lines in your head - but you can always pencil them in, and rub them out later.
- we've only been looking at solutions for the upper left box, so when marking the squares 5 can't go in, we have covered the whole board. We could also have filled in column 6 (because of [6,1]) column 9 (because of [9,2]) and row 7 (because of [2,7]).

Let's look at this board and think about where we could place a 4 in the left hand column.

There's a 4 at position [4,2], so we know there will be no others 4s on this line, and can draw a line across it. There's another 4 at [7,5], so we know are no more 4s on this line either. Finally - and a little differently - there's a 4 at [3,7]. This last 4 is particularly useful as it doesn't just eliminate a single row - it also tells us there are no other 4s in the lower left hand box, thus eliminating *three* squares from the left hand column.

Let's colour in the squares and see what's left in the left hand column. When we eliminate the 8, the 3 and the 7 which are already filled in, we're left with only one square where the 4 could go - [1,6].

Next: counting techniques in Tutorial 2