Challenging Mathematical Problems with Elementary Solutions, Vol. I: 001 (Dover Books on Mathematics)

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.

Challenging Mathematical Problems with Elementary Solutions, Vol. II

In fact, for the most part, no knowledge of mathematics beyond a good high school course is required. Volume One contains 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.

Volume Two contains 74 problems from various branches of mathematics, dealing with such topics as points and lines, lattices of points in the plane, topology, convex polygons, distribution of objects, nondecimal counting, theory of primes, and more. In both volumes the statements of the problems are given first, followed by a section giving complete solutions.

List of unsolved problems in mathematics - Wikipedia

Answers and hints are given at the end of the book. Ideal as a text, for self-study, or as a working resource for a mathematics club, this wide-ranging compilation offers carefully chosen problems that will test the mathematical acuity and problem-solving skills of almost any student, teacher, or mathematician.

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List of unsolved problems in mathematics

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