Mathematical Quickies: 270 Stimulating Problems with Solutions

The best problems conform to the following pattern: 1) Easy to state and understand. 2) Appear difficult to solve and in fact are hard to solve if the approach is wrong. 3) Easy to solve if the proper techniques are applied. All 270 problems in this collection satisfy these criteria. Taken from the `Quickies' column in Mathematics Magazine, these are excellent problems that will tax you if you approach them from the wrong direction. However, once stated, the solution is obvious, and often can be understood by someone with only an advanced high school mathematics background. These problems or their logical variants, form a pool of problems from which you can find many to serve as either challenge problems or even slightly offbeat examination problems. My favorite is the following: Ten letters are placed in ten pre-addressed envelopes at random. What is the probability that exactly nine letters were placed in the proper envelope? The answer is zero, since if nine are placed in the correct envelope the tenth must have been as well. I first read this book about ten years ago and was impressed with the brevity, elegance and at times obvious nature of the solutions. When reading it again in preparation for this review, those emotions were revisited.