Question

Freedonia has fifty senators. each senator is either honest or corrupt. suppose you know that at least one of the free-donian senators is honest and that, given any two free-donian senators, at least one is corrupt. based on these facts, can you determine how many freedonian senators are honest and how many are corrupt? if so, what is the answer?

Answer 1

The only way for any pair of two Free-donian senators to have at least one corrupt senator is for there to be less than 2 honest senators, because if there were 2 or more honest senators, a pair could be picked containing only honest senators. Since we know we have at least 1 honest senator, we know that only 1 is honest and the remaining 49 are corrupt.