The Puzzling Adventures of Dr. Ecco by Dennis Shasha. W.H. Freeman and Company, New York, 1988. Price: $9.95 (paperback).

The best puzzles have always been showcases for beautiful mathematics. Until recently, however, one field of mathematics -- computer science -- has been conspicuous by its absence from puzzledom. You might think that nothing could be farther from math's abstract sparklings than the inexorable bit-by-bit crunching of our favorite machines, but a short course in the theory of computation would change that misguided opinion. Some of the most elegant mathematics of our century has been inspired by computers, and it would come as no surprise to any student of computer science that the field would provide material for some new and wonderful puzzles.

But NYU computer scientist Dennis Shasha is the first to actually write such puzzles -- or at least, the first to write a book of them. The book, called The Puzzling Adventures of Dr. Ecco, contains some 40 problems, nearly all of them drawn from the mathematics of computers, and nearly all of them fresh and exciting. You won't find any of the tired old standbys that ask you to move matchsticks or pennies around; instead, you'll construct digital circuits, design a communication network that still works in the presence of failures, and invent cryptographic protocols for the secure transmission of data. Along the way, Shasha covers many of the key ideas of modern computer science in an elegant, Gardneresque prose. Sometimes the text contains the explanation; but often, the puzzles themselves lead you to discovery. For instance, solving a seemingly innocuous puzzle about ranking tennis players can lead you to a beautiful sorting algorithm. In the solutions at the end of the book, Shasha often reveals the inspiration for the puzzle and refers the interested reader to a paper or textbook. Occasionally, however, no good explanation is provided --the beautiful sorting algorithm is named but never described explicitly, for example --and this is a weakness of the book. On the other hand, it is a book of puzzles, not a teaching text, and judged by those standards provides a fine layman's introduction to the field.

The book relates the adventures of one Dr. Jacob Ecco, omniheurist. An omniheurist, as the book's narrator, Professor Scarlet, explains, is a person who solves all problems. Scarlet first meets Ecco in a bakery when they are both children, where he watches Ecco win a cake from the baker by solving a clever puzzle. The episode sticks in Scarlet's mind, and many years later, upon discovering that Ecco lives not far from his own home, Scarlet seeks him out, befriends him, and learns his story.

After his brilliant doctoral work, Ecco tired of academia moved to MacDougal Street in Greenwich Village, where he earns a living by solving interesting puzzles brought to him by tycoons, generals, engineers, and presidents in various states of desperation. Ecco listens to their problems, presses them for more details, and invariably asks Scarlet, "What do you make of it, Professor?" Scarlet, who plays Watson to Ecco's Holmes, will sometimes offer a suggestion or present a way of understanding a problem, sometimes just comment on the problem's difficulty. Ecco then thinks for a few minutes, scribbles a solution, and hands it to his client. While he is occupied, we, the readers, have the opportunity to solve the puzzle. Ecco's clients are almost always pleased by his solution and usually ask a couple of follow-up questions, which amount to variations on the original puzzle. In solving successively more difficult versions of the puzzle, we are often led to more general ways of looking at the problem.

In between puzzle-solving sessions, there is plenty of time for Ecco and Scarlet to play innumerable games of chess and to discuss topics such as the aesthetics of mathematics, the neural basis of our passion for design, and the foibles of human nature. There's also a bit of jetsetting: Ecco and Scarlet travel to India, and, accompanied by non-monotonic logician Evangeline Goode, they go windsurfing at the Columbia Gorge in Oregon. Shasha's Ecco is a three-dimensional man, not a mere placeholder for genius --we learn about his past, his need for privacy, his love for chess, knowledge and, of course, puzzles, his well-justified fear that he is under surveillance, and his constant striving for elegance and simplicity.

The book even has something of a plot: it gradually becomes apparent that someone or some organization is out to get Ecco. They break into his apartment, leave coded messages that are cryptic, even when decoded, and, in the end, perhaps do something more. Just what has happened at the story's conclusion and who is responsible are the final, unresolved mysteries of the book.

Oh yes, there's also a contest (which runs to the middle of this month): decode 10 messages sprinkled throughout the book and solve the puzzles they describe and you'll be entered in a drawing for a hand-carved chess set. You'll also get a free T-shirt proclaiming you to have joined the great Dr. Ecco in the ranks of that most distinguished and unusual of professions, the omniheurists.

Copyright © 1989, Dr. Dobb's Journal