We present two abstract models of puzzles, permutation puzzles and cyclic puzzles, which can be modelled as puzzle graphs. Based on these models, we implement two puzzle generators and produce various layouts of the puzzles using graph drawing algorithms. Using these puzzle generators we can create new puzzles. Further, we can create new user interfaces of a puzzle by applying different layout algorithms. We implement a method for constructing symmetric layouts of puzzles, as symmetry is the most important aesthetic criteria for the puzzle layout