wo-valued symbols (bits)? Obviously, the first type is the shortest possible, but the symbol is more complex to identify. The second type is longer, but the symbol interpretation the most straightforward. Actually, the choice of symbol representation, by the use of multivalued symbol alphabets, is fully arbitrary. However, for computer implementation, the bit remains the most practical way of coding information. The lesson learnt is that information messages always require an integer number of symbols, the 1/0 bit being the simplest or most elementary type. The bit-measure of information (I), however, is any real positive number. Since the number of required message bits n cannot be less than the information I to be conveyed (n > I); it is, therefore, given by the integer equal to or immediately greater than I. Rényi's fake coin The "fake-coin" determination problem was originally described by the mathematician A. Rényi.° It brilliantly illustrates for the purposes of this entry-level chapter how A. Rényi, A Diary on Information Theory (New York: John Wiley & Sons, 1984), p. 10. Measuring information the information measure can be applied to find the solution of complex optimization problems, in particular, where the outcomes are ternary or multivalued. Let's move directly onto the fun stuff. Assume that a medieval jeweler was presented with 27 gold coins, all looking strictly identical, but with one of them being fake, being made of a lighter metal. The jeweler only has a scale with two pans. What is the minimum number of weight measurements needed for the jeweler to figure out which coin is the fake? Answer: A first hunch comes from realizing that the problem is wholly similar to the 2-faced coin or the 6-faced die examples. All coins presented have equal probabilities, p(1/27), of being the fake one. According to our information-theory knowledge, we conclude that the number of information bits required to identify one out of 27 coins is I = log2 27 = log2 33 = 3 log2 3 bit. We just need to find a technique to 