There are 10 identical bottles of identical pills. Each bottle contains 100 pills. Out of 10 bottles 9 have 1 gram of pills but 1 bottle has pills of 1.1 gram in weight. Given a measurement scale, how would you find the heavy bottle? You can use the scale only once.
Take 1 pill from the first bottle, 2 pills from the second bottle, 3 pills from the third bottle, and so on.
Ideally, you will have 55 pills weighing 55 grams – based on a weight of 1 gram per pill.
The deviation from 55 grams would tell you which bottle contains the heavy pills.
If it is 0.1 gram more, it is the 1st bottle which has the heavy pills. If it is 0.2 grams more, the 2nd bottle has the heavy pills. If it is 0.3 grams more, the 3rd bottle has the heavy pills. If it is 1 gram more, then the 10th bottle has the heavy pills.