Number puzzles have proved an engaging pastime with audiences across the world. Most notably, Sudoku puzzles appear in many newspapers and popular magazines, in a variety of forms, in which varying numbers of clues are provided in incomplete grids. Other mathematical structures have likewise been used as the basis for puzzles based on incomplete grids - for example, Latin Squares and Magic Squares. This article explores the use of Magic Squares with added constraints - the Strictly Concentric Magic Square - for constructing puzzles. In particular, it considers how the strong constraints of the structure affect the number of clues needed for their completion and for providing an enjoyable challenge.