Edit: A problem from an ongoing math competition
Suppose you have a group of 10,000 people where about 5% of them are infected. You have a testing pool machine which can pool up to 32 samples and tell you if one or more people are infected, or none are infected. What is the best strategy to figure out who has the infection that requires the fewest tests, on average.
I've seen similar questions, but in all of them, after identifying the positive group, they then test everyone individually, which seems like an incredible waste of the 32 person pooling machine, especially given the infection rate is relatively low.