I think it's impossible
You enter a room which has ten identical bottles.Each bottle contains hundreds of pills.All bottles except one contain pills weighing 1 gram each.One contains each pill with weight 1.1 gram.You have to find which bottle contains the pills with weight 1.1 gram each.What is the minimum number of times you have to use the scale to find the bottle with pills of 1.1 gram?
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1 solution
First, arrange the bottles on shelf and now take, 1 pill from the first bottle, 2 pills from the second bottle, 3 pills from the third bottle, and so on. Ideally you would have (10)*(11)/2=55 pills weighing 55 grams, when you put the entire pile of pills on the weighing scale.The deviation from 55 g would tell you which bottle contains the heavy pills.
If it is .1 gram more, it is 1st bottle which has heavy pill, if it is .2 more, gram 2nd bottle has heavy pills, if it is .3 more, gram 3rd bottle has heavy pills.