The purpose of mathematics competitions, and in our case the South African Mathematics Olympiad (SAMO), is to promote problem solving skills and strategies, to generate interest and enthusiasm for mathematics and to identify the most talented mathematical minds. SAMO is organised in two divisions--a junior and a senior division--over three rounds.…

The author provides an example of obtaining the correct answer to a problem through a so-called nonsense solution. The conditions under which this incorrect method will yield a correct solution are examined. (JP)

Four unusual mathematics problems with interesting routes to solution are presented. A general method of solution to problems of this type is proposed. (MP)

An analysis is made of overall probabilities of juries making the correct decisions when the juries vary in size from two to beyond five. (DT)

Provided is an analysis, using concepts from geometry, algebra, and trigonometry, to explain the apparent loss of area in the rug-cutting puzzle. (MNS)

Discussed are techniques of presentation and solution of the Classical Cake Problem. A frosted cake with a square base is to be cut into n pieces with the volume of cake and frosting the same for each piece. Needed are minimal geometric concepts and the formula for the volume of a prism. (JP)

Illustrated is the mathematical analysis of a three-dimensional game using techniques from the calculus of finite differences. This game is an analog of the familiar two-dimensional game, Dots and Squares. (JP)

This book is a sequel to MATHEMATICAL CHALLENGES, which was published in 1965. In this sequel are 100 problems, together with their printed solutions. The problems range from those that are quite simple to those that will challenge even the most ardent problem solver, and they include examples from algebra, geometry, number theory, probability,…

Presented are a series of word problems which give students the opportunity to use or develop problem solving skills. The problems are open-ended, with possible answers included. (JP)

Ideas are presented regarding: (1) unique learning activities for students who have difficulty with operations with signed numbers; (2) a mathematical inspection of a unique card trick that can be expressed as an equation; and (3) sketching of graphs of composite trigonometric functions. (MP)

The use of a 25-pin lattice geoboard in a six-week course in middle school geometry is presented, with sample activity cards and test items. Two other ideas discuss the use of algebra in solving verbal problems and teaching negative exponents. (MP)

Clapping music for two performers provides the basis for a series of mathematical problems in combinatorics and group theory. A discussion provides insight about how to avoid overlooking global extrema in constrained max-min problems when solving systems of algebraic equations. (JJK)