Here is a beautiful problem:
Given twelve coins, exactly two of them is radioactive. There is a machine. You are able to put some of the coins into the machine, and then the machine tells if the coins contain a radioactive one. It doesn’t tell exactly how many, only if there is at least one. How many tries do you need to find the two radioactive coins.
Of course is it easily possible with 12 or 11 tries. But what is the minimum number of tries needed to find the two radioactive coins? And what if there are $n$ coins, where two of them are radioactive? Then is it possible to find the minimum number of tries?