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.