Play has been discussed by mathematicians and mathematics educators as essential to mathematical progress and has been widely acknowledged to have a role in learning. Yet, play is rarely acknowledged, leveraged, or studied for mathematics learners beyond early childhood. Moreover, there are theoretical and empirical challenges with designing for…

In this article, I present a collection of puzzles appropriate for use in a variety of undergraduate courses, along with suggestions for relevant discussion. Logic puzzles and riddles have long been sources of amusement for mathematicians and the general public alike. I describe the use of puzzles in a classroom setting, and argue for their use as…

To understand better some of the classic knights and knaves puzzles, we count them. Doing so reveals a surprising connection between puzzles and solutions, and highlights some beautiful combinatorial identities.

"Instant Insanity II" is a sliding mechanical puzzle whose solution requires the special alignment of 16 colored tiles. We count the number of solutions of the puzzle's classic challenge and show that the more difficult ultimate challenge has, up to row permutation, exactly two solutions, and further show that no…

One of Gardner's passions was to introduce puzzles into the classroom. From this point of view, polyomino dissections are an excellent topic. They require little background, provide training in geometric visualization, and mostly they are fun. In this article, we put together a large collection of such puzzles, introduce a new approach in solving…

The Spider and the Fly puzzle, originally attributed to the great puzzler Henry Ernest Dudeney, and now over 100 years old, asks for the shortest path between two points on a particular square prism. We explore a generalization, find that the original solution only holds in certain cases, and suggest how this discovery might be used in the…

The Borough of Manhattan Community College (BMCC) in New York City is fourth among all community colleges in awarding degrees to minority students and in awarding degrees to African Americans. The BMCC student body is approximately 37 percent Hispanic, 33 percent black, 15 percent white, and 15 percent Asian. In addition, a significant proportion…

The blue-eyed islanders puzzle is an old and challenging logic puzzle. This is a narrative of an experience introducing a variation of this puzzle on the first day of classes in a liberal arts mathematics course for non-majors. I describe an exercise that was used to facilitate the class's understanding of the puzzle.

In this article we show how the Sudoku puzzle and the three simple rules determining its solution can be used as an introduction to proof-based mathematics. In the completion of the puzzle, students can construct multi-step solutions that involve sequencing of steps, use methods such as backtracking and proof by cases, and proof by contradiction…

We introduce a simple game made up of a board of coins on a triangular lattice. We then study the possibility of turning the board from one pattern of heads and tails to some other pattern. Given that a solution exists we find a precise answer to the number of solutions possible. We then generalize this to more complex boards with coins of many…

The "N" queens problem is a classic puzzle. It asks for an arrangement of "N" mutually non-attacking queens on an "N" x "N" chessboard. We discuss a recent variation called the "N" + "k" queens problem, where pawns are added to the chessboard to allow a greater number of non-attacking queens to be placed on it. We describe some of what is known…

Computers are very good at solving certain types combinatorial problems, such as fitting sets of polyomino pieces into square or rectangular trays of a given size. However, most puzzle-solving programs now in use assume orthogonal arrangements. When one departs from the usual square grid layout, complications arise. The author--using a computer,…

The basis of a good mechanical puzzle is often a puzzling mechanism. This article will introduce some new puzzling mechanisms, like two knots that engage like gears, a chain whose links can be interchanged, and flat gears that do not come apart. It illustrates how puzzling mechanisms can be transformed into real mechanical puzzles, e.g., by…

In this article, a systematic approach is given for solving a magic star puzzle that usually is accomplished by trial and error or "brute force." A connection is made to the symmetries of a cube, thus the name Magic Hexahedron.

Two mathematical brainteasers, with solutions depending on involved trial-and-error processes, are shown to have ingenious solutions. (MP)