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The Puzzles of Mars is a puzzle book intended for bright or gifted young people in grades 8 through 12. The book is a fictional tale about a mathematician from Earth who travels to the planet Mars to share and exchange puzzles with Martians at the Martian Academy of Sciences. Most of the puzzles appear to be difficult, yet they have simple, ingenious solutions. Some of the puzzles require a little mathematical skill, though not much beyond what is usually taught in American grade schools. The main focus is on puzzles that are based on important mathematical ideas and concepts. Each puzzle is a special instance of deep, important mathematical ideas like symmetry, invariance, parity, and relative motion. A Notes for Teachers section is included with ideas and questions to stimulate classroom discussion of mathematical ideas and concepts.