The Mathematics of Oz: Mental Gymnastics from Beyond the Edge
This is an excellent collection of mathematical problems and puzzles at all levels of mathematical sophistication. The tasks are presented to little Dorothy by Dr. Oz, a mathematically obsessed alien. Dorothy tries to solve problems, each described via a nice story: this motivates the reader to solve the challenge. Full solutions are presented in the ‘Further Exploring’ part of the book.
The problems cover various topics: geometry and mazes, sequences, series, sets, arrangements, probability and misdirection, number theory, arithmetic and the physical world. As an example, consider the following problem: ‘Can you divide a triangle into finitely many triangles to produce all acute internal angles?’ The reader is guided to think about many interesting areas, and various methods are exploited and presented in a non-traditional way. The author has written many interesting books, and his website www.pickover.com is well known.