Presented are solutions to variations of a combinatorics problem from a recent International Mathematics Olympiad. In particular, the matrix algebra solution illustrates an interaction among the undergraduate areas of geometry, combinatorics, linear algebra, and group theory. (JJK)

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)

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)

An approach to using the method of least squares, a scheme for computing the best-fitting line directly from a set of points, is detailed. The material first looks at fitting a numerical value to a set of numbers. This provides tools for solving the line-fitting problem. (MP)

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)

Several sample problems from the "Ladies Diary," published in the early 1700s, are reviewed. They provide a fascinating glimpse of the mathematics considered useful in the eighteenth and early nineteenth centuries. (MP)

This resource book contains mathematical games, tricks, and quick activities for the classroom. Categories include place value, number lines, basic facts and computation, computation and calculator practice, puzzles for tricky thinkers, and geometry. Ten classroom games and activities are found in the place value and number line sections, 27…

The application of the Hamilton method for apportioning seats in the United States House of Representatives is presented based on the 1980 census. It is felt that this method is preferable to the equal proportion method currently used if for no other reason than the greater appearance of fairness. (MP)

Two kinds of secret writing, codes and ciphers, are discussed. The weakness of a ciphering system mentioned in the March 1981 issue is pointed out, and an alternate method is presented. Programs written in BASIC are presented which can be used to encipher messages and help break ciphers. (MP)

Five problems on the generation and study of prime and related numbers are discussed. Solutions to the problems posed will be in next month's presentation. (MP)

A discussion of the mathematics of rugby is related to an earlier article about mathematics and the physical world. (MP)

This document consists of three modules concerned with aspects of statistics. The first provides knowledge of the effect of imperfect correlation and random error on differences between means, and the reasons for the necessity of random allocation of objects to experimental and control conditions in scientific experimentation. The second unit…

An activity is described as an example of an application that draws on the behavior of current in electrical circuits to create a symbolic algebra. Five worksheets are included, with discussion of their use. (MNS)

The game of Yahtzee is analyzed to some extent through methods of elementary probability. Several different problems are posed, and these serve to illustrate both mathematical concerns and game play strategy. Solutions are provided to all questions at the conclusion and suggestions for further questions are presented. (MP)

A brief introduction to the broad field of curve-fitting is provided to help explain the reasoning behind least-squares data fitting, and also to provide useful equations for two functional forms of interest in chemistry. Appendices give program examples written in Fortran and detail the method of Guggenheim. (MP)