Suppose you have a cloth bag with one marble inside-either black or white, you don't know which. You add a white marble, shake the bag, and take a marble at random. It's white. What are the odds that the remaining marble is white? Obviously 1/2, right? Wrong. The correct answer is 2/3. This is just one of the scores of intriguing puzzles and paradoxes in this fascinating book. Lewis Carroll's diverse interests ranged from inventing new games like "arithmetical croquet" to important problems in symbolic logic and propositional calculus. He was famous for his puns, anagrams, acrostics, and riddles and is believed to be the author of a poem that reads the same vertically as horizontally. Some of his word puzzles remain unsolved to this day. His mathematical humor included instructions for folding a handkerchief into a variant of the Klein bottle, as well as "proof" that if a bag contains two marbles that must be either black or white, there will always be one black and one white.Just as Carroll was the preeminent recreational mathematician of his time (perhaps of all time), Martin Gardner is the preeminant writer on recreational mathematics of our time. He is the ideal guide for this fun and informative tour of Carroll's inventions.Martin Gardner's previous books on Lewis Carroll and his works include The Annotated Alice and More Annotated Alice. Mr. Gardner is also the author of many books on magic and recreational mathematics, and for many years wrote the "Mathematical Recreations" column for Scientific American.