You have 1000 possible Covid vaccine candidates. You need to test them and find out if one works as quickly as possible. The test is to apply a small drop of a vaccine candidate to a sample, and wait to see if the Covid virus is compromised. The tests are very expensive and time-consuming, so you want to perform as few as possible. Since the tests are time-consuming, you only want to do one round of testing.
What is the fewest number of tests to confirm:
If there is a single working vaccine, identify which one it is.
If there is more than one working vaccine, then identify that situation as well. (Since that would be good news, it is OK if more testing is needed to root out the particulars of that).
It is assumed one can provide multiple vaccine candidates to a single sample. For example, if you apply three different candidates to one sample, and the sample is not compromised, then you know none of those candidates work. On the other hand, if the sample is compromised, then you know that at least one of the three samples work, but not which one(s).