Suppose you have 1000 unlabeled vials, and you want to know whether it’s T or E inside. Since you’re not a chemist, you decide to test on passoids to find out which vials contain which hormone. You know that, if injected with any amount of Testosterone, the passoid kills herself within 24 hours.
*Edit: Forgot to mention but only 1 vial contains T, the rest contain E. You only have 1 day to figure out which vial is T.
What is the minimum number of passoids you need in order to guarantee that you can label the T vial? Explain your test process as well
hint: each vial contains enough to inject multiple times
are you looking for 10? since log base 2 (1000) ≈ 10? if so, what method would you use to be completely sure, since I don’t think you could get it guaranteed with a worst case using only 10 passoids in a single day. I see that the limit as you get more days is 10 passoids used, but i dont think you could hit it in one day
you’re on the right track! there’s a method to do it in a day though
wait! i do see it actually! thats interesting!! i might be too combinatoricsbrained right now but it made sense to me when i realized you need 10 bits to represent one thousand in binary. also here’s a diagram.