Sunday, July 10, 2011
COIN MACHINE WEIGHING
you have 20 coin machines, each of which produce the same kind of coin. you know how much a coin is supposed to weigh. one of the machines is defective, in that every coin it produces weighs 1 ounce less than it is supposed to. you also have an electronic weighing machine. how can you determine which of the 20 machines is defective with only one weighing? (by one use, we mean you put a bunch of stuff on the machine and read a number, and that's it -- you not allowed to accumulate weight onto the machine and watch the numbers ascend, because that's just like multiple weighings). you are allowed to crank out as many coins from each machine as you like.
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weigh a different number of coins from each machine, and find the difference between the expected weight and the actual weight. let us pretend machine 7 is the defective one.
ReplyDeleteadd one coin from machine one. add two coins from machine two. add three coins from machine three, etc. up to twenty coins from machine twenty. the expected weight would be X + 2X + 3X + ... + 20X = 210X, but the actual weight would read 210X - 7oz. therefore, machine seven is the defective one.