Logic Riddles

Question: A man murders his wife with a knife in their car. Nobody is around to see this. He throws her out of the car being careful not to leave any fingerprints on her body. Next he throws the knife off of a cliff into a gorge where it will never be found and he goes home. An hour later the police call him and tell him that his wife has been murdered and he needs to come to the scene of the crime immediately. As soon as he arrives, he is arrested.

How did they know he did it?

Question: Which eight-letter word still remains a word after removing each letter from it?

Question: what can go up a chimney down but cant go down a chimney up

Question: Nary a tick, nary a tock- silent, silent, the handless clock. Tarry no longer; cast off all doubt. The sands of time are running out.

Question: A wise person was once sentenced to death by a king. The king couldn't decide how to execute him so he said to the wise person, you can say anything you want, if it is true, I will hang you, if it is not true I will shoot you. In the end the king released the wise man. What did the wise man say?