$\textbf{Defective Machine}$
A company has $10$ machines that produce gold coins. One of the machines is producing coins that are one gram lighter. What is the minimum number of weighs you will need in order to find out the defective machine?
$\textbf{Solution}$
One weigh is sufficient. Take one coin from the first machine, two coins from the second machine, ..., ten coins from the last machine. If their total weight is one gram short, then the first machine is defective. If it is two grams short, then the second machine is defective, and so on.
$\textbf{Analysis}$
While $10$ weighs must be sufficient, it is almost for sure not the answer. To qualify as a brain teaser, the required number of weighs is likely to be a very small number. A good guess should be $1$. The solution also shows that the number $10$ is not significant either. The answer will be the same if there are $100$ or more machines.