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Star Battle

Place an equal number of stars (indicated by the number next to the puzzle) on every row, in every column and in all larger areas such that two stars never touch, not even diagonally.

In some cases, the thick area boundaries extend outside the diagram, or go through rows or columns without stars. In such cases, they are marked by dotted lines.

Example

There will be only one star on the bottom row, but also there will be exactly one star in the right half of the bottom row. Therefore with the right mouse button, we can mark the left half as being empty.

Now suppose the star in the 3rd column is on the 2nd row. All squares of the area in the upper right corner are neighbours of this star, and as a consequence none of them will contain a star itself. Because every area needs a star we can mark the square in the third column on the 2nd row as empty.

In the 1st column there will be a star on either the 2nd or the 3rd row, so we can mark both the 2nd and 3rd square in the 2nd column as empty. Now the area spanning most of the middle two columns has only one valid position for a star left. We will fill it in and mark all other squares on its row and column as empty.

Similar reasoning helps to mark the rightmost square on the 3rd row as empty, leaving only one option for the rightmost area. Marking the rest of it's row and column as empty leaves only two positions for the remaining two stars.

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