# The Magic Garden of George B and Other Logic Puzzles

###### Raymond Smullyan
Publisher:
World Scientific
Publication Date:
2015
Number of Pages:
170
Format:
Paperback
Price:
29.00
ISBN:
9789814678551
Category:
General
[Reviewed by
Megan Patnott
, on
03/16/2016
]

Raymond Smullyan’s The Magic Garden of George B And Other Logic Puzzles was originally published in 2007 by Polimetrica, and has been reprinted by World Scientific in 2015. Like some of Smullyan’s other books, it begins with several chapters of logic and arithmetic puzzles and then introduces the reader to an idea from mathematical logic through an analogy, presented in a series of interconnected chapters. In The Magic Garden, Smullyan aims to introduce the reader to Boolean logic. The switch from puzzles to Boolean logic is very clear, with the puzzles in the first half titled “Book I” and Boolean logic in “Book II.”

Nine of the twelve chapters of puzzles are primarily logic puzzles and the remaining three chapters are primarily arithmetic tricks. The reader hoping for typical Smullyan-style puzzles, such as the knights and knaves and puzzles involving the inhabitants of various islands, will not be disappointed. The puzzles in each chapter usually have some connection to each other, although only a few of the chapters include a narrative component. The chapters themselves are not connected to each other. Good, clear solutions to the puzzles are included at the end of each chapter. My only complaint with this half of the book is that some of the puzzles are really what Smullyan calls “monkey tricks,” even outside of the first chapter (whose title at least clearly warns the reader to expect some trickery).

The second half of the book introduces the reader to Boolean logic through an analogy with a magical flower garden. Flowers in this garden are either red or blue, and there are a number of rules about flowers that do or don’t exist (for example, for every flower $A$ there exists another flower $B$ that is blue exactly when $A$ is red). The reader is asked to use these rules to prove facts about the garden in a series of problems. The solutions to these problems are given at the end of the each chapter, and through solving them the reader discovers many facts about Boolean logic. After a few chapters in the garden, Smullyan adds islands populated with people who follow rules similar to those governing the gardens in order to introduce isomorphisms. The last six chapters are more explicitly mathematical, introducing first propositional logic and the Boolean algebra of sets before generalizing to Boolean algebras and ending with notes on history and applications.

The Magic Garden does not assume the reader has any formal mathematical training beyond high school. However, a reader without prior experience with mathematical logic would likely benefit from having done the logic puzzles in the first half of the book before tackling the second half. I think a motivated general reader would enjoy the garden and island analogy chapters, but may find the notation in the last six chapters overwhelming. A handful of Exercises, adjacent to the main series of Problems, are included to help the general reader build their skills, but the lack of solutions to these Exercises seems likely to frustrate their target audience. The biggest issue, though, are the typos. Some of them are harmless, but others are likely to be very confusing to a mathematically inexperienced reader.

Due to the typos, I would not use it as a supplementary reading in a course and would hesitate to recommend it to most students. I have found it a useful source of enrichment activities, though, and if you are a fan of Smullyan’s other works, you will find much to enjoy here.

Megan Patnott is an Assistant Professor of Mathematics at Regis University in Denver, CO. Her training is in algebraic geometry and commutative algebra.

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• The Knight-Knave Disease
• Human or Android?