Expert: Chanda Walker - 3/15/2009

Question
In a certain mythical community,a stranger meets three other natives and asks them, "How many of you are politicians?" The first native replied, "We are all politicians". The second native replied, "No, just the two of us are politicians". The third native said, "that isnt true either" Was the third native a politician?

i have my answer, just want to have a second opinion before i confirm my answer to the class. thanks so much

Answer
Sorry about the delay--my wifi went wonky.

So I think we have to make these assertions:
1) All politicians lie (or at least say untruths) all the time.
2) All non-politicians tell the truth.

I feel comfortable doing that since one sentence says that both the others are not true.  So SOMETHING has to be false here.

Any way. . .

Native 1 and 2 both claim to be politicians.  So if they are NOT politicians, they are lying.  But we have claimed non-politicians tell the truth.  So they must be politicians and their claims must be false.

For the first claim to be false one of Native 2 or 3 must not be a politician but we already know native 2 is a politician so native 3 must not be a politician.

Let's check in on claim number 2.  It says that just the two of us are politicians.  In order for this to be false, he must be referring to natives 2 and 3 not natives 1 and 2 as the "us."

Since we've proved claim 1 and 2 are false then claim 3 is true and we have a non-politician!

Let me know if I can be of further assistance!