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Download Baffling Brain Teasers by Gardner M. PDF

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By Gardner M.

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08 at the end of the first year. In fact, at the end of every year the value of the investment is multiplied by this factor. 08 is an example of an annual multiplier. 496M Continuing in this way, we see that the list of values of the investment at the yearly anniversaries is 32 Recalling The 1999 item represents the current value of the investment: in other words, about 53 trillion dollars. Q. Isn 't it far-fetched to use this calculation to make a conclusion about the Louisiana Purchase? A. Although our calculation is rough, it supports the contention that the French were not cheated when they agreed to the Louisiana Purchase for only 15 million dollars.

The digits of the decimal expansion/rom some point on are completely determined by the current remainder. Interesting Numbers 51^ Q. It seems to me that the digits are always determined by the remainders. Why do you say "from some point on"? A. The situation is a bit more complicated. At some point in the long division algorithm, we "bring down" only zeros to append to the remainder. Therefore, itis only after this point that the current remainder determines, without reference to the digits of the quotient, (1) the next digit of the quotient and (2) the next remainder, and so on.

Q. What's geometric about this? Why is it called a geometric progression ? A. The ancient Greeks were first to use this term. The most likely reason is that certain geometric magnitudes such as the length of the diagonal of a unit square, a one-by-one square, did not fit the Greek concept of number. Geometric magnitudes were considered conceptually different from arithmetic magnitudes. 11). 12) if the first and last terms are known. The middle term of this three-term geometric progression is called the geometric mean of the first and last terms.

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