Question: 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?
Answer: 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.
Question: A man is found dead on a Sunday morning. His wife calls the police immediately. The police question the wife and staff. The wife said she was asleep, the cook said he was cooking breakfast, the gardener said she was picking vegetables, the butler said he was cleaning the closet, and the maid said she was getting the post. The police immediately arrested the murderer.Who was the murderer?
Answer: The maid because there's no post on Sundays.