hw1 - k using at most 15 drops Prove that your answer...

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Math 55 - Homework 1 Due Friday, June 24, 2011 Directions: You are encouraged to discuss homework with fellow students. However, you should write up all solutions alone. Your answer should be clear enough that it explains to someone who does not already understand the answer why it works. (This is different than just convincing the grader that you understand.) 1. Section 1.2, problems 46 through 51 2. Section 1.4, problem 52 3. The Weston Watermelon Company has managed to develop an especially durable wa- termelon. They have hired you to determine the exact durability of these super water- melons. Weston’s offices are in the 100-story Pasteque building in San Francisco. They want to know the least number k , so that their watermelons will break when dropped from the k th floor. Unfortunately, they only have have two test watermelons for you. Come up with a sequence of experiments which is guaranteed to determine
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Unformatted text preview: k using at most 15 drops. Prove that your answer always works. Fine print: All of Weston’s watermelons behave exactly the same. When dropped from the same floor, they always break or always survive. If a watermelon breaks, it cannot be used again. If a watermelon survives a fall, it is totally unaffected by the fall. Extra Credit: Prove that it is not possible to always determine the answer with less than 15 drops. 4. You are given twelve gold coins and a balance. The coins look and feel identical to you. However, you know that one of them weighs a slightly different amount. The other eleven are all the same weight. Using the balance at most three times, determine which coin is different. (As a warm-up, try finding a bad coin among four in two weighings.)...
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This note was uploaded on 03/14/2012 for the course MATH 55 taught by Professor Strain during the Summer '08 term at Berkeley.

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