I first subscribed to Games Magazine in junior high school. I renewed it every year until I went to college, when I started changing addresses so often that it was too much of a pain in the ass. It's probably the best puzzle periodical (bimonthly, unfortunately) there is except for the fact that they kept my last subscription check and didn't bother to send me any magazines for it. Inexplicably, they don't have a Web site. Maybe publications that cater to actual use of the brain really can't support themselves in this country.
One of the puzzle games I first found in Games (like Battleships) is called Paint by Number here, though it originated in Japan. It sounds a little cheesy and juvenile, but it's actually pretty challenging. Just like Battleships, the number of blackened squares are listed for each row and column. The idea is to deduce where they go in order to form a picture. Again, because it's a logic puzzle, it seemed like it would be pretty easy to teach the computer how to solve it. I still kept struggling with the translation from human logic to code.
I tried all kinds of solutions, from a genetic-style fitness algorithm to straight logic combined with random guessing to brute force search. None of these were effective, but I still wasn't a very good programmer back then, either. Some time later, I found a site dedicated to Paint by Number, with its own Java applet complete with solver. At some point I may compare notes with the developer, but if I remember correctly, that solver can't solve every puzzle, just the ones that fit certain constraints. I think mine's prettier, anyway.