A method of using vector analysis is presented that is an application of calculus that helps to find the best angle for tacking a boat into the wind. While the discussion is theoretical, it is seen as a good illustration of mathematical investigation of a given situation. (MP)

Competitions at one high school are described: they try to attract as many participants as possible, not just excellent students. In one type, creativity is stressed; another is a tournament; a third involves problem solving activities. Examples are included. (MNS)

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

A history of perfect numbers is presented, which briefly covers the 27 values known at this time. (MP)

The goals and history of the Mathematical Olympiads for Elementary Schools are described. Teams, levels, and gender are discussed, as well as teacher training, administration, scoring, and awards. Sample problems are included. (MNS)

The Australian Mathematics Competition was designed around the content of common school mathematics, and thus is intended for almost all mathematics students, not just exceptional ones. The competition's conceptual and organizational basis and the three levels of competition papers are described. Sample questions are included. (MNS)

Problems with apportioning seats within the House of Representatives every 10 years are discussed. The history of the problem and the nature of the politics involved are reviewed, and the current method in use is detailed along with its flaws. A call for a more sensible system is made. (MP)

Described is an experience in assigning mathematics problems that have been purposefully selected from professional journals to assist upper level college mathematics students in developing confidence in their ability to contribute published solutions. Several examples are included. (JJK)

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

A problem in applied mathematics is presented that is thought fit for a study project by secondary students. The analysis includes topics in beginning algebra, theory of interest, and theory of sums of series of infinite length and looks at trade-offs between price and mileage. (MP)

Methods for solving logic puzzles which focus on thought-free procedures that facilitate solution are discussed. Two of the procedures noted pertain to the interior of any submatrix, whereas others span several submatrices. A puzzle is presented at the conclusion as an exercise for practicing the methods promoted. (MP)

An exploration of a problem called solving quadratic congruences modulo p is detailed and is built around an alternate method of deriving the quadratic formula. Three practical pedagogical values that have been experienced by students and instructor when the material was presented to classes are noted. (MP)

High school students are warned against service station fraud. A problem-solving section is designed to help students calculate consumer costs for various fraudulent transactions. Several ways of reducing fraud or of lessening the chances of problems are noted. (MP)

The famous birthday problem is discussed and activities which can be used with it as an introduction to probability are examined. (SD)