Another Heads-Up for Puzzlers
The book is definitely worth looking at, but, perhaps as a function of its ambition to teach some important (and cool) math along the way, it is rather difficult on the whole, and ridiculously so in some cases (one of his 'puzzles' is to disprove the Borsuk conjecture, a problem that had been open for something like 60 years. Granted, there is a hints section, but come on...). The Amazon page lets you browse a number of the more approachable puzzles, so check it out.
The second is 'Mathematical Mind-Benders', Peter Winkler's much-anticipated sequel to the instant classic 'Mathematical Puzzles: A Connoisseur's Collection'. I haven't spent enough time on the new one to see how it stacks up to its predecessor, but it definitely contains some beguiling problems. Many are 'old friends' of the puzzle genre (bugs, prisoners, hats, etc.), but remade and fiendishly harder--think of the fight with Super Shredder at the end of 'Turtles II'...
However, while Winkler's books are also quite hard, they generally involve much less 'higher math' than Bollobas', which is really written for readers interested in mathematics proper. Another emphasis of Winkler's new book is on surprise answers, as in the following two puzzles from the first, warm-up chapter:
-A pencil has a regular pentagon as its cross-section, and its maker's logo on one face. If the pencil is rolled on a table, what is the probability that it comes to rest with the logo facing up?
-You have 15 bags. How many marbles do you need to produce an arrangement where each bag contains a different number of marbles?
Winkler also unveils a neat word puzzle called 'the HIPE game', something he co-invented as a teenager. One player comes up with a string of letters and challenges the other players to find a word containing it (as a block of adjacent letters): for instance, can you place HIPE in a word? Of course, the problem poser should actually have a word in mind...
Some other challenges he gives: BG, CM, FC, FW... and the book has many more (and harder). I'm normally pretty decent at word games, but this one is killing me so far.
Thanks, Bollobas and Winkler!