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Thread: Heavy Stuff

  1. #1
    Plutonium Lounger
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    Re: Heavy Stuff

    A is fairly easy.

    First weighing: <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Put 3 bottles in each pan. If one of these is heavier then it contains the heavy bottle, otherwise the remaining set of 3 does</span hide>
    Second weighing: <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">From the set of 3 known to contain the heavy bottle. Put one bottle in the left pan and one in the right. If one of these is heavier then it is the required bottle, otherwise the third one is.</span hide>

    StuartR

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    Plutonium Lounger Leif's Avatar
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    Re: Heavy Stuff

    B - though I'm not sure if this counts as a single weighing:
    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold"> Take the 8 known 'OK' botles from the first set. Add one to the left scale and add one of the second set to the right scale. If they balance, continue until you either have a mis-balance - pointing to the recently added bottle on the right pan - or the remaining bottle from the second set is the heavy one.</span hide>

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    5 Star Lounger Ruff_Hi's Avatar
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    Re: Heavy Stuff

    Stuart - spot on.
    Leif - interesting but I don't think that is an single weighing either (thinking about it, I don't think I have given you enough info in the original post - see above)
    (Location Australia, then UK, but now USA. Heart, outlook, attitude, etc always Australian)
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    5 Star Lounger Ruff_Hi's Avatar
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    Heavy Stuff

    <P ID="edit" class=small>(Edited by Ruff_Hi on 06-Nov-05 07:50. Added the weight of the contaminated pills in [img]/forums/images/smilies/cool.gif[/img])</P>I was visiting my half sister (the one who owns the rattle snake, not the one with the short leg) the other day. She had three sets of nine bottles, each bottle with 20 pills in it. One bottle from each set contained pills that are contaminated (ie they are too heavy). She also has some measuring scales (the balance type like the blind lady justice).

    A) Find the heavy bottle from the first set using no more than two measures on the scales

    [img]/forums/images/smilies/cool.gif[/img] Find the heavy bottle from the second set (these pills are heavy by 5% - weighing 105 milligrams) using no more than one measure on the scales

    C) Find the heavy bottle from the third set without using the scales.
    (Location Australia, then UK, but now USA. Heart, outlook, attitude, etc always Australian)
    Quote: "All Happiness is the release of internal pressure"

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    WS Lounge VIP sdckapr's Avatar
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    Re: Heavy Stuff

    B <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">If I can use the balance to actually determin the weight with pills on one side standard weights on the other:
    Add 1 pill from bottle 1, 2 from bottle 2, 3 from Bottle 3, etc on the left side
    On the right side add 45 pills from the "normal" bottles from set 1

    Determine the additional weight that needs to be added to the right side to balance them and divide it by 105 mg. The number will be the bottle number containing the heavy pills</span hide>

    Steve

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    WS Lounge VIP sdckapr's Avatar
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    Re: Heavy Stuff

    <P ID="edit" class=small>(Edited by sdckapr on 06-Nov-05 10:12. Added PS)</P>C<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Take a container of water that is completely full with discharge tube in it and a container to collect any overflow.

    Just submerse Jar 1 into the water and collect the water. remove the jar and Refill the water. Repeat for each one. The jar which displaces the most water is the heaviest and has the contaminated pills.

    If you do not want to catch the overflow, you can use an underfilled container and just note the level increase with each jar. the one with the highest displacement is the heaviest.</span hide>

    Steve

    PS
    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">I could also just use my analytical balance to get their weights and not use the pan balance</span hide> <img src=/S/smile.gif border=0 alt=smile width=15 height=15>

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    5 Star Lounger Ruff_Hi's Avatar
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    Re: Heavy Stuff

    Steve - correct for [img]/forums/images/smilies/cool.gif[/img]

    Re C) - I don't think that sticking the bottles in water will work if the bottles all sink. The bottles are all the same size and will displace the same amount of water. It is a good answer if the bottles don't fully sink - however, isn't is close to weighing? Can you think of another solution?

    <img src=/S/whisper.gif border=0 alt=whisper width=29 height=17>I have my rudi hat on and I am thinking of a specific answer that you have to try and work out - lol
    (Location Australia, then UK, but now USA. Heart, outlook, attitude, etc always Australian)
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    Plutonium Lounger Leif's Avatar
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    Re: Heavy Stuff

    C:
    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Assuming they are soluble and the weight is proportional to volume, put one pill from each bottle into a glass of water and see which takes the longest to dissolve.</span hide>
    or
    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Assuming they are slimming pills, find twenty equally overweight mice and feed each a different pill. The one that loses the most weight has been fed the heavier pill.</span hide>
    or
    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Drop one pill from each bottle onto something bouncy and see which bounces up the highest.</span hide>
    or
    <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">Tie a piece of thread to a pill from each bottle. Get Jezza to make up a Newton's Cradle from old lolly sticks and see which pill knocks the others the most.</span hide>

    <img src=/S/whisper.gif border=0 alt=whisper width=29 height=17> Well, you did mention Rudi...

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    WS Lounge VIP sdckapr's Avatar
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    Re: Heavy Stuff

    I assumed the bottles were the same size. Thus the heavier ones will displace more liquid (Archimede's principle) since they have a higher overall density (mass / Volume). Whether they sink or not is immaterial, they still displace the volume of water based on the weight of object.

    Steve

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    Plutonium Lounger
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    Re: Heavy Stuff

    If the bottles sink then they displace their own volume of water, they only displace their own weight if they float.

    StuartR

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    5 Star Lounger Ruff_Hi's Avatar
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    Re: Heavy Stuff

    <img src=/S/laugh.gif border=0 alt=laugh width=15 height=15> <img src=/S/rofl.gif border=0 alt=rofl width=15 height=15> ok, ok, ok - I was looking for "send one pill from each bottle to the lab for testing."

    However, I don't know what this is ... a Newton's Cradle ... I understood the part about Jezza and paddle-pop sticks, but Issac's Cradle???

    I found this but would that work with heavy (or not so heavy) pills?
    (Location Australia, then UK, but now USA. Heart, outlook, attitude, etc always Australian)
    Quote: "All Happiness is the release of internal pressure"

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    WS Lounge VIP sdckapr's Avatar
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    Re: Heavy Stuff

    <img src=/S/blush.gif border=0 alt=blush width=15 height=15>Brain fart.

    Though I do think if they have air in the bottles they should float...

    Steve

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