My favorite iPhone game lately is Trainyard, a puzzle based on getting trains of various colors to their proper stations. Trains come in six colors, and depending how you set up the tracks you can merge, say, a red train and a blue train into one or two purple trains, or split a green train into one blue and one yellow. As you get into the more difficult puzzles, there are usually several specific things you need to make happen, often in a particular order, to get to the right combination of colored trains, and the puzzle is how to make them happen and then get the trains to their stations, when you have what seems like nowhere near enough space for laying down the track you need to accomplish all these things. The key is often finding ingenious ways of having trains use the same track to get to different destinations without interfering with each other.
I’ve solved all the original puzzles and am now about two-thirds through the new batch of forty bonus puzzles — I’m working on them in order and the next one to tackle is “Trinidad”.