Solving a 2-star 10x10 Star Battle puzzle
A tutorial by Krazydad
Here's how to solve a 10x10 Star Battle puzzle. This is the puzzle I'm solving, which is Puzzle #4 from from Volume 1, Book 2.
In these 10x10 puzzles, each row, column and bolded region must contain two stars. The stars can't touch each other, not even diagonally.
The first thing you'll notice is that there is a small region that consists of three horizontal cells. This essentially a freebie, as there is only one way to place the 2 required stars in this region. We can't use the middle cell, because it is adjacent to both the left and right cells, so we rule that out and put the stars in the remaining two cells. Then we can mark the surrounding (touching) cells, as well as the remaining cells in the row. Note that I'm using marks to indicate cells that can't contain a star -- the cells that I'm ruling out. In these puzzles, you'll typically make a lot of these marks.
Now take a look at the small region that I've highlighted in yellow. The external cell indicated by the blue question mark can't contain a star, because it would rule out every single cell in the region. Similarly, the internal cell indicated by the red question mark can't contain a star either - because it would rule out every other cell, and prevent us from placing our 2nd star. This divides the region into two parts, each of which must contain a star. One of those parts is a lone cell, so it must contain a star. The other part, containing two cells, must contain the remaining star for column 1, so we can eliminate the other cells in that column.
These other two small regions that I've highlighted are under similar constraints. On the top right, we can divide the region into two parts, and place a star. We can also eliminate the two middle cells from the center region, as well as the two cells immediately above and below it.
Now, on the long hilighted region, we've eliminated all but two cells, and can put stars in them. Once you put a star in column 10, notice that that the top two cells of column 10 must also contain a star, so we can eliminate all the other cells in column 10.
The hilighted region on the right has been reduced to 4 open cells, and has a forced 2-star placement. This completes column 8. After you place those, you'll find that row 3 has only two open cells remaining and can be filled in with stars. This will lead to other easy stars. At this point, the rest of the puzzle falls pretty easily.