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A is fairly easy.
First weighing: 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
Second weighing: 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.
StuartR
(Edited by Ruff_Hi on 06-Nov-05 07:50. Added the weight of the contaminated pills in 
)
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
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.
(Edited by sdckapr on 06-Nov-05 10:12. Added PS)
CTake 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.
Steve
PS
I could also just use my analytical balance to get their weights and not use the pan balance 
Steve – correct for
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?
I have my rudi hat on and I am thinking of a specific answer that you have to try and work out – lol
C:
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.
or
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.
or
Drop one pill from each bottle onto something bouncy and see which bounces up the highest.
or
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.
Well, you did mention Rudi…
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?
Brain fart.
Though I do think if they have air in the bottles they should float…
Steve
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