So there are some ideas going around how to make testing for Corona more efficient, given resource and time limits on testing. One idea is to bulk test groups of people by simply mixing their bio samples, and quarantine everyone in case the test turns up positive. That way you'll be able to contain the virus with relatively few tests.

But this idea can be pushed further: what if we combine samples of lets say 100 people, and in case of positive, divide the group in two groups of 50, and re-test both groups, etc. Of course keep in mind that in this example, if a bulk test gives a positive, there can be more than one person who is positive.

So this can be solved analytically, but I suck at math: How do you find every infected person in a population of N people, while minimizing the number of tests? A safe assumption here is that if N is the total population of a country, there will be at least one person who's infected.