There is a party of 100 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?
1 of them is honest and 99 of them are liars.
One of them is honest satisfying the first piece of information. For the second statement to be true, the remaining politicians have to be liars.