Interactive Mathematics Miscellany and Puzzles (Cut-The-Knot.com) This Interactive CD, based on Alexander Bogomolyny's Web page, contains a whole lot of fascinating material. The particular sections I've listed below are among the simpler, which should appeal to kids age 10-14 or so. Arithmetic and Algebra: Breaking Chocolate bars. How few breaks do you need to break a bar into individual squares? Here you can figure out the rule for yourself, and see various games and magic tricks based on the solution. Fun with Digits. Starting with the sequence 123456789, insert plus or minus signs between digits so that the result of the arithmetic operation will be 100. Factorials and Division. Guess the missing digit of a number that's formed by multiplying all the numbers from 1 to 21. Prof. Bogomolny's answer is clear and logical, and gives one a hint of how to go about solving mathematical problems. Fast Arithmetic tips. Here are some simple and helpful rules for doing arithmetic. Mathematical Proof. The proof given here has to do with a word puzzle, not with numbers. But the discussion does a good job of getting you to think about proofs. Number Guessing game. You choose a number between 1 and 99, and the computer correctly guesses your number after asking you a few questions. The Pigeonhole Principle. Is this true? "At any given time in New York City there live two people with the same number of hairs." Self-reference. Here are some amusing sentences aimed at perplexing you. Geometry Disappearing Lines. What happened to the missing line? Halving a Square. Here's a neat story having to do with a square with another square inside it. The Greek philosopher Socrates explains how to compute the area of the smaller square. The Moebius Strip. This segment contains one of Maurice Esher's famous drawings, along with an animated picture of a Moebius strip rotating. Pythagorean Theorem. Here are 28 lovely visual proofs of the famous theorem. Games and Puzzles The Three-glass puzzle. Given three glasses containing 8, 5, and 3 cups. Given that the 8-cup glass is full. Can you separate out four cups by pouring from cup to cup? A Baffling Prediction describes a neat and simple card trick. The Game of Fif. Play against the computer to see which of you is first to choose three numbered squares adding to 15. A Matter of Age. Here's a simple magic trick that let's you guess a person's age. Squares and Circles is a neat game that'll make you think. Probability Bear cubs problem. Given a black and a white bear, we figure the likelihood that both are male, given various known fact. This problem will help you think about some very tricky aspects of probability.