These brainteasers are challenging--a little too challenging I feel. Most of them require serious work, at least for a casual puzzler and layman, and the reader could use some formal math training or a strong affinity for geometry. These puzzles are distinctly harder than the ones in, say, Martin Gardner's Entertaining Mathematical Puzzles. In other words most of Barr's puzzles are not the kind of brainteasers where you (the casual puzzler) sort of mull it over for 5 to 20 minutes and either get it or don't; these are not the kind of puzzles that you think through on a short drive or in the shower or on a coffee break.

To give you an idea, here's a typical one, on p. 54: "A draftsman has no instruments but a compass and a sheet of paper which he does not fold, and which can be bought at any stationer's. How does he establish and mark the 6 vertices of a regular hexagon with only ONE placing of the point of the compass?" The answer (yep, looked it up) is NOT one where you're going to go "oh, of course!", that is, not unless you're a pretty hardcore puzzle type with a serious interest in geometry. Or how about this one (p. 37): "Any or all of the faces of tetrahedron may be right triangles, with the right angles distributed in various ways. Obviously no two right angles can be in the same face .... What are the restrictions in the case of a tetrahedon which has only three right angles, with two at one apex, and the 3rd at another? Give proof." Whoah! That is a typical brainteaser in this volume. In fact calling them "brainteasers" gives the wrong idea. Many of the solutions sort of resemble excerpts of diagrams and equations from Newton's Principia. (I'm exaggerating but not that much.) Well I think I'm a reasonably intelligent guy ... was good at math through calculus.... And maybe, MAYBE, I could start to chip away at some of these, but it starts to feel like a chore .... The only respite here is a section in the back called "Submiscellany of short puzzles, more or less from everyday life", which are more common sense questions or Jeopardy-type questions.... (Even here some of the questions are a bit off, for example "What transparent object becomes less transparent when wiped with a clean cloth? It is found in many households" The answer is an object that is not that common.)

I'd say that, if you enjoy the level of puzzles in Gardner's slimmer Dover books, or e.g. Emmet's Puzzles for Pleasure or Erwin Brecher's Ultimate Book of Logic Puzzles & Brainteasers, and are looking for more of the same, you ought to be warned that most of Barr's puzzles here are another order of difficulty and complexity. I give it 4 stars as nevertheless I'm sure there are people --either more dedicated puzzlers or much smarter than me or both--for whom this book is ideal.