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

Elucidated is the relationship among three threads of mathematical investigations: Kirkman's schoolgirl problems, finite geometries, and Euler's n-square officer problems. (JP)

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)

The problem of determining the number of squares on a checkerboard is extended to finding the number of rectangles on an n x n board and finding the total numbers of cubes and rectangular solids in an n x n x n cube. (DT)

A series of problems is presented that (1) focus on certain kinds of numbers or (2) emphasize a specific concept of number theory. Several are appropriate for extensive investigation with a computer. (MNS)

Young children benefit from activities that involve various partitions of numbers, especially the number 10. Presented are two activities that require students partition and recombine numbers to solve problems in a gamelike situations. Examples and worksheets are provided. (MDH)

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)

A discussion of some number patterns which arose from a consideration of the number of diagonals of a general polygon. (MM)

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)