The study of number puzzles has fascinated mathematicians and others for thousands of years. These studies reveal much about the way our number system is constructed. Studies of number puzzles also often produce new methods of mathematical thinking and new computer programming techniques. These classic number puzzles are explained in the following paragraphs.

Triangles

Many people know that 3² + 4² = 5². There are many other combinations of three whole numbers that have the same property, such as 5² + 12² = 13² and 7² + 24² = 25². These numbers are called Pythagorean triples because of the property of right triangles known as the Pythagorean Theorem (after the Greek mathematician Pythagoras).

Since the time of the early Greeks, mathematicians have known of a way of generating any number of Pythagorean triples. If m and n are any two integers, then a triangle with sides X, Y, and Z can be "generated" by these formulas:

m²- n² = X

2mn...