BuddyLee
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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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| 07-31-2002 02:48 PM |
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JD Heel
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What you do is take a different amount of coins from each machine to be weighed in the entire group of coins.
Thus, if you took one coin from the first machine and your final amount ended up one ounce less than the target amount (what it would be if no machine was defective), then you know it's from that machine. If you are six ounces short, then it's whatever machine you took six coins from.
-JD
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| 07-31-2002 03:42 PM |
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BigBiscuit
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</font><blockquote><font size="1" face="Verdana, Helvetica, sans-serif">quote:</font><hr /><font size="2" face="Verdana, Helvetica, sans-serif">Originally posted by BuddyLee:
you are allowed to crank out as many coins from each machine as you like.</font><hr /></blockquote><font size="2" face="Verdana, Helvetica, sans-serif">Take one coin from machine one, two coins from machine two, three coins from machine three....etc and put them on the machine.
Total weight if all coins were good is X.
The weight will be X - n * (one ounce). Where n is some integer and the number of the bad machine.
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| 07-31-2002 03:46 PM |
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BuddyLee
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There you go, right on.
To be more specific, you should number the machines one to twenty, then take one from machine one, two from machine two... etc.
Your answer is right, but I just thought I'd make it more clear.
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| 07-31-2002 03:46 PM |
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BuddyLee
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Looks like BigBiscut got there before I could. Good answer, nice formula.
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| 07-31-2002 03:48 PM |
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BigBiscuit
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Thanks,
But I thought I was posting the ANSWER first. I hate that JD Heel.
BB
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| 07-31-2002 03:51 PM |
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JD Heel
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Don't worry -- the person who gets the ROTD first wins nothing. I put a lot more stock into being the first to win that lucrative NASCAR nickel pool....
-JD
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| 07-31-2002 03:58 PM |
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