text: Thirty five years ago my high school (Thomas Jefferson, in Federal Way, Washington) held annual competitions in mathematics.  They did it in the form of a test that came bound in a small white booklet, just was a few pages long.  There weren't many questions, perhaps a dozen or two (usually in the form of story problems), but they required deep thought and concentration (at least for me).  I still remember the feeling of excitement and trepidation as I took the "white book" and opened it to the first problem.  Several hours later I'd consider myself accomplished if I'd managed to completely answer more than half the questions.  
  
  Ian Stewart's book reminds me of those tests.  Here's a sampling of what's inside:
  
  1)Mrs. Anne-Lida Worm decides she wants a new couch, and tells Mr. Worm to get it for her, while she goes shopping for a new tight for baby Wermintrude.  But Anne-Lina doesn't want just any couch.  She wants the biggest possible couch that can be carried down the hall in their house, and around the 90-degree hall at the end.  What shape does the couch have, and how big is it?  This is a truly riveting story.  Will Mr. Worm solve the couch problem in time?  
  
  2)Alberto wants to conduct tests on grapes, evaluating the influence of different soils.  He wants to conduct experiments to see how different soils and exposure to the sun affects the quality of wine.  His land is on a hillside, though, which is narrow, so he can plant only three varieties of grape on each plot of land.  How can he arrange things so that he tests all seven varieties of grapes when they are arranged so that each plot contains exactly three different species, where any two plots have exactly one variety in common, and any two varieties lie in exactly one common plot?
  
  Sixteen chapters make up this book.  Though their titles are whimsical, the mathematical problems aren't.  Some are still unsolved.  Even though these problems fit in what would probably be called recreational mathematics, they are fiendishly cleaver with solutions, and developed insight along the way, that are at once challenging and rewarding.  Here's a sample of some of other topics discussed in Stewart's book:
  
  How might one transport a lion, llama, and head of lettuce in a boat, across a lake, without leaving any two species where one might eat the other in the absence of a caretaker?  How can you calculate the temperature and entropy of a curve?  How can one even talk sensibly about a curve having temperature and entropy in the first place?  Suppose that you need to tile a room, and the tiles come in odd shapes.  Is there anyway to know if the tiling problem has a solution?  Can mathematics tell us things about evolution, such as whether or not evolution comes gradually or in spurts (or both)?  
  
  This is a fun, lighthearted book, but the mathematical problems and puzzles it discusses will really make you think.  I enjoy reading as I exercise on my elliptical machine.  I get double the sense of accomplishment when I can read and workout at the same time.  Ordinarily, I can estimate how long I've been on the machine by how many pages I've read - 20 pages in 40 minutes is about average.  But with Stewart's book I had to be careful.  Several times I found that I'd worked out for an hour and only managed to cover half-a-dozen pages or so.  
  
  If you love mathematics, particularly mathematical puzzles, then this is a book you'll really enjoy.  It has many problems for the reader, with answers at the back of each chapter.  If you do the problems and understand everything in the book, in detail, it will occupy many hours of your time.  All in deep thought and utter enjoyment.   
  