THE LADY OR THE TIGER?

Smullyan is a tease and a provocateur--as readers of What Is the Name of This Book? and This Book Needs No Title already know. This elegant professor of mathematical logic (Lehman College, CUNY) does not overwhelm you at the start, unlike Martin Gardner in the ever-challenging puzzles in Scientific American. Smullyan offers more homely fare, old chestnuts and new cashews that are idiotically easy to comprehend, but are traps for the unwary. You will either succumb to the first ""Suppose you and I have the same amount of money. How much must I give you so that you have ten dollars more than I?""--or you will disdain further perusal. If bitten, you are invited to pursue a succession of problems in simple arithmetic or logic. In the title chapter, the suitor faces two doors each bearing statements which are either true or false--and tip the logical thinker as to the whereabouts of the lady. Move on, then: to the asylums whose doctors tell only the truth the whole truth and nothing but the truth--but whose inmates invariably lie; to Transylvania, where humans can tell hollies and vampires no truths; and to various picturesque isles of questioners or dreamers. Finally, come metapuzzles: a species in which there is a dangling bit of information which, if you know it, can solve the problem. The point of all this may be didactic: the puzzles grow deeper, longer, more complex. But if you have pressed on vigorously and profited from Smullyan's clear-cut solutions, you may experience small frissons of delight as you follow him into the dizzying heights of GÖdel's proof and the very nature of proof, truth, and logic in mathematics. It's heavy-going, sometimes, but with a wonderful conclusion: ""mathematical thinking is, and must remain, essentially creative. Or, in the witty comment of mathematician Paul Rosenbloom, it means that man can never eliminate the necessity of using his own intelligence, regardless of how cleverly he tries."" Many will rise to the bait.