Challenge problems

Challenge Problems

Problem 1

One hundred mathematicians are invited to the castle of Dr. Evil. Before entering the ballroom he gives each mathematician a hat with 7 accurate digits of pi on the front. No one sees their own hat but they are all told that at least one person has 7 accurate digits of pi on their hat. Next Dr. Evil tells them to walk into the ballroom and stand in a circle so they can see every other mathematician. He tells them