The showman comes to a river and finds a small boat that holds only himself and one passenger. For obvious reasons, he can't leave the wolf alone with the goat, or the goat with the cabbages. How does he get his cargo safely to the other side (see "Tricky Crossings").
Such puzzles and their many variants are ways of dressing up a relatively straightforward mathematical problem. Since the days of ancient Egypt and Babylon, instructors have often used such devices to turn routine mathematical exercises into problems that tickle and challenge the mind (see "Problems to Sharpen the Young" and "The Ladies' Diary").
Mathematical puzzles and games remain remarkably popular. Puzzle addicts throughout the world snap up many of the hundreds of such books published every year. A wide range of magazines feature puzzle pages, often including sudoku and other venerable time sinks.
The appearance of a new, ingenious puzzle can stir up frenzied activity. In just three years after its introduction, sales of Rubik's cubes grew beyond 100 million.
Amusement is one of humankind's strongest motivating forces. Although mathematicians sometimes belittle a colleague's work by labeling it "recreational" mathematics, much serious (and useful) mathematics has come our of recreational problems, which test mathematical logic and reveal mathematical truths.
Philosopher and mathematician Bertrand Russell noted, "A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science."
Probability theory originated in questions about gambling. Ingenious solutions to tiling problems are seen in the folk art of many cultures and in physical theory for describing crystals.
Similar connections between recreational problems and important mathematical questions occur in number theory, geometry, graph theory, and many other areas of mathematics.
Mathematical physicist John L. Synge summed it up. "In submitting to your consideration the idea that the human mind is at its best when playing, I am myself playing, and that makes me feel that what I am saying may have in it an element of truth."
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