Freedonia has 50 senators. Each senator is either honest or corrupt. Suppose you know that at least one of the Freedonian senators is honest and that, given any two Freedonian senators, at least one is corrupt. Based on these facts, you can determine how many Freedonian senators are honest and how many are corrupt.

Question

Mathematics

Patricia Garrison

26 February, 19:53

Freedonia has 50 senators. Each senator is either honest or corrupt. Suppose you know that at least one of the Freedonian senators is honest and that, given any two Freedonian senators, at least one is corrupt. Based on these facts, you can determine how many Freedonian senators are honest and how many are corrupt.

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Answers (1)

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Conor Dickson · Answer 1

There are 49 corrupt senators and 1 honest senator.

Step-by-step explanation:

Freedonia has 50 senators. Each senator is either honest or corrupt. At least one of the Freedonian senators is honest.

As we can see that there are no two senators where both of them are honest. So either there is one senerator who is honest or none.

As given that at least one of the Freedonian senators is honest.

Hence, we can conclude there is one and only one honest senator.