Please take a look at the following sentence from an LSAT:
if one of the cities contains exactly two hospitals and exactly one university, then which one of the following lists three cities that might, among them, contain no hospital?
After checking some explanations of this sentence, they all mention that the sentence actually asks to identify three cities that none of which contain a hospital.
I thought that "among" means "one or some of a group", so this sentence should be read as asking to identify three cities that some of which could have contained no hospitals.
I would really appreciate your help. Thank you very much for your time.