There is a party of 100 high-powered politicians. All of them are either honest or liars. You walk in knowing two things:

– At least one of them is honest.

– If you take any two politicians, at least one of them is a liar.

From this information, can you know how many are liars and how many are honest?

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I agree with Manjush – but expect within a short time the one honest person will either quit or also become a liar. :(

I like this puzzle.

When you take the two politicians, you can ask either one “is the other guy honest?” and if he says “Yes” you know they are both liars. But if you get the answer “no” it is either the honest guy saying the other guy in the room is a liar, or it’s the liar falsely saying the other guy is also a liar.

To figure out which is which you can then ask almost any question you know the answer to. “Is today Monday?” The person who answers correct is the honest one.

I’m wondering if there is one question we could ask either one of the two people in the room and know if the honest guy is in the room, and which one he is?

One honest politician. If there were two or more the second statment would be incorrect.

has to be one honest politician and 99 lying politicians.

Manjush is today’s winner!

Yes, from the information you know 1 is honest and 99 are liars. One of them is honest satisfying the first piece of information. Then if you take the honest man and any other politician, the other politician must be a liar to satisfy the second piece of information, ‘If you take any two politicians, at least one of them is a liar.’ So 99 are liars.