Mr. Jacoby has compiled a group of mathematical problems selected for their ability to stimulate interest and imagination in those so oriented. Advanced mathematical knowledge is not a necessity. Among the contributors is the dean of puzzle composers Hubert Phillips, known to many as Caliban. Each chapter contains several anecdotal problems followed by complete and lucid examinations and explanations. Each set is introduced with relevant material. Included is a short history of written numeration, an introduction to the fundamental operations of algebra, an explanation of the science of probability, inferential deductions (a month in the country should accompany each of these pure and not so simple experiments in pure logic), and Diophantine equations (fun with trial-and-error, with an emphasis on the latter). Though the problems are fascinating, Mr. Jacoby might have drawn a clearer line between those necessitating use of formula and those which can be done with the free mind. They're all tough.