Here are the first three puzzles in Chapter 1 of Raymond Smullyan's lovely book The Lady or the Tiger?: 1 • How much? 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? 2 • The Politician Puzzle A certain convention numbered one hundred politicians. Each politician was either crooked or honest. We are given the following two facts:(1) At least one of the politicians was honest. (2) Given any two of the politicians, at least one of the two was crooked. Can it be determined from these two facts how many of the politicians were honest and how many were crooked? 3 • Old Wine in a Notsonew Bottle A bottle of wine cost ten dollars. The wine was worth nine dollars more than the bottle. How much was the bottle worth?
