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Topic: Chemist - Trying to find good pills from bad pills (Read 554 times) |
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Venk
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Chemist - Trying to find good pills from bad pills
« on: Jun 11th, 2003, 9:36pm » |
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Heres a puzzle:
Data:
1) A chemist has n bottles of pills with him.
2) m of these bottles contain only good pills.
3) n-m contain of these bottles contain only bad pills.
4) A good pill weighs x grams and a bad pill weighs y grams.
5) The chemist has a weighing scale and can use this just once.
6) There are infinite number of pills in each bottle.
Can the chemist identify the bottles with good pills from those with bad pills in just one weighing? If yes, how? If no, why?
- A simplified version of this problme is when m=1. In this case we take i pills from each bottle where i ranges from 1 to n. Then compute the bottle with good pills. This maybe trivial, however I find this modified version of the problem (above) challenging.
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towr
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Re: Chemist - Trying to find good pills from bad p
« Reply #1 on: Jun 11th, 2003, 11:20pm » |
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does the chemist know the values of x,y and m?
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BNC
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Re: Chemist - Trying to find good pills from bad p
« Reply #2 on: Jun 11th, 2003, 11:39pm » |
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I think you have to know the values of x and y - otherwise you may diffrintiate "good" from "bad" -- but won't be able to state which is which - and that's not very helpful, now is it?
I think we may do without m:
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Take 1 pill from box 1, 2 from 2, 4 from 3 ... 2^(n-1) from box n. Weight. Compare to the weight of "all good pills" measure. The difference is Dw. Denote dw = x-y. Now, take the binary repesentation of Dw/dw. The "1" bits are the locations of the bad pills.
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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