The last two weeks have gotten a fair number of comments - many positive, but many calling the puzzles "too easy". There are many good reasons to start slowly when constructing a new type of puzzle, or in introducing new types to an unfamiliar audience. One of my reasons is that I recently began to cross-post these puzzles on Wired's Decode blog (under the series title "Dr. Sudoku Prescribes") and I felt my sometimes brain-busting content was not the right way to start. Some puzzles, like the regular but easy Shikaku, were simply elegant solves even if the challenge was lower than usual. Well, I've revisited the themes of the last two weeks to offer this "booster shot" of puzzles. I still haven't taken these puzzles to crazy extremes, but here are (hopefully) more challenging versions of the recent Star Battle and Shikaku puzzles. Enjoy!
Place stars into some cells in the grid so that each row, column, and region contains exactly two stars (in the example, just one star). Stars cannot be placed in adjacent cells, not even diagonally.
Divide the grid below into rectangles so that all cells belong to one rectangle and so that each rectangle contains one numbered circle. The numbered circle must indicate the area of the rectangle, not counting any of the gray cells, as seen in the following example.