Mathematical Puzzles: A Connoisseur's Collection

Mathematical Puzzles: A Connoisseur's Collection by Peter Winkler is not your casual puzzle book. Even though most of the problems inside are easy to formulate, many of them require extensive mathematical background and well-developed analytical thinking. If you possess these two qualities however, you will certainly enjoy this book. The puzzles are hard, the solutions are beautiful and the explanations are very well-written. The book contains over 100 puzzles which are split in different categories - Insight, Numbers, Geometry, Geography, Algorithms and others. In order to give you an idea of what to expect, I have selected several puzzles from the book, which represent its overall level.

1. Given 10 red points and 10 blue points on the plane, no three on a line, prove that there is a matching between them so that line segments from each red point to its corresponding blue point do not cross.

2. A phone call is made from an East Coast state to a West Coast state, and it's the same time of day at both ends. How can this be?

3. The hour and minute hands of a clock are indistinguishable. How many moments are there in a day when it is not possible to tell from this clock what the time is?

4. Associated with each face of a solid convex polyhedron is a bug which crawls along the perimeter of the face, at varying speed, but only in the clockwise direction. Prove that no schedule will permit all the bugs to circumnavigate their faces and return to their initial positions without incurring a collision.

For me personally, MP:ACC is the most valuable puzzle book in my collection. If you are up to the challenge it offers, you owe yourself a favor to buy it. Even if you don't feel too confident in your abilities to solve the problems in it, you can still get it and study the solutions. All the brilliant ideas which you will find inside are priceless.