This article will describe two activities in which students conduct experiments with random numbers so they can see that having at least one repeated birthday in a group of 40 is not unusual. The first empirical approach was conducted by author Cauto in a secondary school methods course. The second empirical approach was used by author Flores with…

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 involving the use of diagrams to depict plangers'' (in which lines cross a specified number of times) are discussed. (LS)

The possibility of non-transitivity of preference choices is discussed. One example each from voting and from sports demonstrate some conditions where transitivity does not hold. Suggestions are made for using this type of problem in the classroom. (LS)

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)

Nine problem situations involving the use of random numbers are given. Topics include cooking, hunting, bacteria contamination, waiting lines, ransom walks, and branching. In addition to the problem situation, questions are suggested which can be used to extend the investigations. (LS)

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)

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)

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)

Looks at the solution to the mathematical-modeling problem asking students to find the smallest percent of the popular vote needed to elect a President. Provides assumptions from which to work the problem. (MDH)

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)

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

Proposes the utilization of graph theory to solve optimization problems. Defines the notion of spanning trees and presents two algorithms to determine optimization of a spanning tree. Discusses an example to connect towns by power transmission lines at minimum cost. (MDH)

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)