Question

Freedonia has 49 senators. Each senator is either honest or corrupt. Suppose you knowthat at least two of the Freedonian senators are honest and that, out of any threeFreedonian senators, at least one is corrupt. Based on these facts, can you determinehow many Freedonian senators are honest and how many are corrupt? if so, what is theanswer?

Answer 1

There are 47 corrupt senators and 2 honest senators.

Explanation:

Freedonia has 49 senators. Each senator is either honest or corrupt.

At least 2 of the Freedonian senators are honest and that, out of any 3 Freedonian senators, at least 1 is corrupt.

As we can see that there are no 3 senators where all of them are honest. So either there is one senator who is corrupt and 2 are honest.

Also it is given that at least two of the Freedonian senators are honest.

Hence, we can conclude there are 2 honest senators and 47 corrupt senators.