Five hundred mathematical challenges

This book contains 500 problems that range over a wide spectrum of areas of high school mathematics and 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 and taught by the book. For many problems, more than one solution is supplied so that students can see how different approaches can be taken to a problem and compare the elegance and efficiency of different tools that might be applied. Teachers at both the college and secondary levels 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. These problems were first published as a series of problem booklets almost twenty years ago, at a time when there were a few resources of this type available for the English reader. They have stood the test of time and the demand for them has been steady. Their publication in book form is long overdue. This collection provides a solid base for students who wish to enter competitions at the Olympiad level. They can begin with easy problems and progress to more demanding ones. A special mathematical toolchest summarizes the results and techniques needed by competition-level students. -- from back cover.