I know there's been a good amount written on COVID-19 pool testing, but I think my question is slightly different.
Suppose your PCR machine can pool a maximum of 32 samples and test it. If you know that there are two sick people in a group of 1000 people, what's the minimum number of tests that can be done, given that each test must be made beforehand?
What I mean by "made beforehand" is that each pool to be tested is independent of each prior test.
Note, in you algorithm, you have to always correctly figure out which two people have the disease.
This question is one on an active qualifying quiz for Math Camp.
Zixuntau, you bloody well know it is absolutely unethical for you to post any of the currently active quiz questions in anypublic or private math forum, or to seek any help from anyone. You have to sign an oath stating that your submitted answers are yours and yours alone, without help or assistance from anyone online or in person. I suppose you will not have a problem swearing that a lie is the truth. You didn’t have a problem dragging us into your cheating scheme.
Your cheating has also made it easier for others to cheat, and that will potentially keep dozens of honest, deserving students from receiving advanced mathematical training and education.
You should suspend your math education and take a few ethics classes. Maybe you will learn how fucking a mathematical (or any) education institution can have ramifications that affect large segments of society or the world at large for decades to come. Maybe then you will actually give a damn.