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Which gives more information, five 3-choice questions or eight 2choice questions? 6. How many 2-choice questions do you need to identify 1000 categories? Combinatorics Suppose we use only 3-choice questions, so that we can code each answer with A, B, or C. Each card will have a code word like ABBA C, giving us a classification of the cards. If there are n questions, then how many categories are there? ' Let an be the number of such sequences. Let A x be the set of all sequences which begin with A, Bx the set of all which begin with B, and Cx the set of all which begin with C.

Then, when you want to look something up, you, a clerk, or a computer could search through the cards for the kind of papers you want. For the sake of simplicity, we could record each answer with a single symbol at a certain standard spot on the card. However the first question above would then not be suitable. How would a paper on the solutions of the equationx 2 + y2 = z 2 , which also discussed the Pythagorean theorem be classified? A and G cannot both be printed on the same spot. So the questions should have mutually exclusive answers.

Nevertheless, the slide rule has several advantages for teaching purposes. 5 A class project: the slide rule 41 to see how the results are obtained. On the other hand, the slide rule is open to inspection and, with some study, the user can find out exactly how it works. It can also be used to exhibit a concrete representation of the logarithmic function. It is a useful and interesting project for a class or a mathematics club to make their own slide rule. Afterwards, the students may compare their homemade slide rule with a commercial one, if one is still available.