Artificial Intelligence can be thought of as the study of machines that are capable of solving problems that require human level intelligence. It has frequently been concerned with game playing. In this thesis we shall focus on the areas of search and complexity, with respect to single-player games. These types of games are called puzzles. Puzzles have received research attention for some decades. Consequently, inter-esting insights into some of these puzzles, and into the approaches for solving them, have emerged. However, many of these puzzles have been neglected by the artificial intelligence research community. Therefore, we survey these puzzles in the hope that we can motivate research towards them so that further interesting insights might emerge in the future. We describe research on a puzzle called LEMMINGS that is derived from a game called Lemmings, which itself is in NP-Complete. We attempt to find the first success-ful approach for LEMMINGS. We report on a successful approach to a sub-problem