Five Hundred Mathematical Challenges
MAA, 1995 - Mathematics - 227 pages
This book contains 500 problems that range over a wide spectrum of mathematics and of levels of difficulty. Some are simple mathematical puzzlers while others are serious problems at the Olympiad level. Students of all levels of interest and ability will be entertained by the book. For many problems, more than one solution is supplied so that students can compare the elegance and efficiency of different mathematical approaches. A special mathematical toolchest summarizes the results and techniques needed by competition-level students. Teachers will find the book useful, both for encouraging their students and for their own pleasure. Some of the problems can be used to provide a little spice in the regular curriculum by demonstrating the power of very basic techniques. The problems were first published as a series of problem booklets almost twenty years ago. They have stood the test of time and the demand for them has been steady. Their publication in book form is long overdue.
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ABCD angle arithmetic arithmetic progression assume bers chords coefficients congruent convex convex polygon cube Determine diagonals digital sum digits distance distinct divides divisible equal equation equilateral triangle factor FIGURE four geometric given greatest common divisor Hence hexagon induction inequality inscribed intersect isosceles Klamkin Law of Cosines Law of Sines least least common multiple length Let ABC locus Mathematical midpoint modulo multiple nonnegative obtain pairs parabola parallel parallelogram perpendicular Pigeonhole Principle plane players points polygon polynomial positive integer possible PQRS Problem produced Prove quadratic quadratic residues quadrilateral radius rational real numbers relatively prime respectively result follows Rider right-angled roots satisfy Second solution sequence Show Similarly sin2 sphere square Suppose symmetry tangent tetrahedron Theorem tion triangle ABC triangle inequality vertex vertices yields