10 bottles of pills

This is a pretty popular brain teaser with many companies.

On the shelf you have 10 identical bottles of identical pills (let’s say there’s a hundred pills in each bottle). However, one of those 10 bottles contains cheap knockoff pills. The only way to differentiate fake pills from real pills is the weight - while real pills weigh 1 g each, the knockoff pills are only 0.9 g. You have one scale that shows the exact weight (down to the mg) of whatever is weighed.

How can you tell which bottle contains fake pills with just 1 weighing?

Answer: 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 55 pills weighing 55 grams, when you put the entire pile of pills on the weighing scale.

However, that won’t be the case, since some pills are only 0.9 g. The deviation from 55 g would tell you which bottle contains the fake pills. If you’re off by 0.9 g, it must have been the first bottle, if you’re off by 1.8 g, it must have been the second bottle, and so on.