Logic Riddles

Question: There are two ropes that both take exactly 1 hour to burn from end to end. You are unable to cut the rope. How can you burn the two ropes in a total of 45 minutes?

Question: If it takes three men two days to dig a hole, how long does it take one man to dig half of a hole?

Question: People see through me, but none pass through without killing me. I can be anywhere, and can be seen double or single. What am I?

Question: There are 100 prisoners lining up to go to jail. Each prisoner is wearing a hat that is either black or white. The prisoners don't know their own hat color, just the hat color of those in front of them in line (the first prisoner in line can't see anyone's hat and the last prisoner can see everyone's hat except their own). Starting from the back, one of the guards asks each prisoner what color their hat is. If they are correct they get to go free but if they are wrong they go to jail.If the prisoners get to discuss a plan, how can at least 99 of them be saved?

Question: A person has one lion, one lamb and a bundle of grass. He wants to cross a river but there is only one boat and it can't sustain the weight of more than two articles at time. Also, he has to make sure that the lion doesn't eat the lamb and the lamb doesn't eat the grass. How will he get to the other side of the river with all three intact?