Challenging Mathematical Problems with Elementary Solutions I

Volume I: Combinatorial Analysis and Probability Theory
Volume II: Problems from Various Branches of Mathematics

Designed for advanced high school students undergraduates graduate students mathematics teachers and any lover of mathematical challenges this two-volume set offers a broad spectrum of challenging problems — ranging from relatively simple to extremely difficult. Indeed some rank among the finest achievements of outstanding mathematicians.
Translated from a well-known Russian work entitled Non-Elementary Problems in an Elementary Exposition the chief aim of the book is to acquaint the readers with a variety of new mathematical facts ideas and methods. And while the majority of the problems represent questions in higher ( non-elementary ) mathematics most can be solved with elementary mathematics. In fact for the most part no knowledge of mathematics beyond a good high school course is required.
Volume One contains 100 problems with detailed solutions all dealing with probability theory and combinatorial analysis. Topics include the representation of integers as sums and products combinatorial problems on the chessboard geometric problems on combinatorial analysis problems on the binomial coefficients problems on computing probabilities experiments with infinitely many possible outcomes and experiments with a continuum of possible outcomes.