congrats to u/null and u/very_silly_gal for being the first ones to get it! lmk if this was fun or if i should post more puzzle questions like this

the answer: you only need 10 passoids to be able to find the vial of T. The key idea here is that having a binary outcome (lives or dies) gives you 1 bit of information, so for 1000 vials 10 people is enough to store info for 2^10 = 1024 outcomes.

the process ends up being that you can treat each passoid as 1 bit, and 10 passoids as a length 10 bit string. label each vial from 1 to 1000 in binary, and inject that vial into the corresponding passoid. eg. vial 0100100010 would be injected in the 2nd, 5th and 9th passoid. the next day, you can tell which vial has T based on which passoids die