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: There is a farmer who has three sons. Nearing his death, he asked his three sons to find two objects that can fill the room he's in. The one who can deliver will be chosen as his heir. So the oldest son goes to the market to get hay while the middle son go get leaves. The youngest son goes to a shop and buys two things that he put in his pocket. The oldest son's hay only fills half the room, the middle son's leaves fills 2/4 quarters of the room, while the youngest fills the room with his two objects. Question: What are the two objects that the youngest son used to fill the room?
Answer: A match and a candle.