I need to solve a riddle
You have 10 bottles with 100 pills in each of them. In 9 of the
bottles, each pill weighs 10mg. In one bottle,each pill weighs 9mg.
These pills are poisonous.You have a digital scale that reads out in
mg. Can you determine which bottle contains the poison with only one
weight measurement?

hi polo59,
Assuming "one weight measurement" implies you can only use the digital
scale one time, then the solution i offer, is as follows:
You place all bottles onto the digital scale. You know each of the 9
bottles (each containing 100 non-poisonous pills) will weigh 1000mg
plus the weight of the bottle itself (say 50mg). So, the total weight
of these 9 bottles will be (1000+50)X9 = 9,450mg. (weight per bottle
incl. pills =1050mg). The bottle with the poisonous pills will weigh
950mg (900+50). Therefore, one can assume that the total weight of all
10 bottles (including the one containing the poisonous pills) will be
10,400mg, assuming the weight of the bottle is a known and constant
factor. Since you know that the weight of each bottle (with the
non-poisonous pills) is 1,050mg, then you can expect the measurement
on the scale to reduce by this amount as you lift each bottle off the
scale. If you find that measurement on the scale has reduced by 950mg,
(as opposed to 1050mg), then you will have discovered that that bottle
contains the poisonous pills, as it weighs less than 1050mg. If all
the nine bottle that you have lifted off the scale have reduced the
total weight by 1050mg each time, then you can assume that the last
remaining bottle will be the one containing the poison, and the
digital scale should show the weight of that bottle to be 950mg.
 
I hope that my above explanation is clear, and that i have helped you
solve the riddle.

Depends what you mean by "one measurement" but one way to do it:  dump
the pills on the scale one bottle at a time and watch the digital
readout each time: it will be multiples of 1000 mg until you get to
the poison pills, which will give a readout that ends in 900 mg.

Assuming that you can only use the scale once (i.e. you can't use
pafalafa's solution), there is still a way to weigh all pills at once,
and still differenciate with regards to which ones are contributing to
a lesser weight.

To do this, you take 1 pill from the first bottle, 2 pills from the
second bottle, and so on.  If all pills weighed 10mg (if there were no
poison pills), then there would be 10*(1+2+...+10) = 550mg of pills. 
However, let's say the 2nd bottle has poison pills in it.  Then two
pills would be 9mg, and the total weight would actually be 548mg.  For
every poison pill, you will get one less milligram of total weight. 
Because only one bottle has poison pills, you can weigh all the pills,
and subtract the weight from 550.  This will index into the different
bottles, and tell you which has the poison.

WOW jaacob-g.  That's a good one!

More than a  'good one'.

Jaacob's comment is the solution. The answer given is not.

GA does not has a good mechanism for dealing with this situation,
which happend from time to time.