There was once a teacher who wanted to punish his misbehaving students by torturing them with a very boring math problem. he told them to get out a piece of paper and add up all the number 1 to 100. the students groaned but got to work adding up all the numbers. imagine the teacher's surprise though when fred (who was a big goof off but very good in math) raised his hand after about 30 seconds and said i've got it. and he did. can you, like fred, figure out a way to solve this problem simply, without having to sit there and add numbers for an hour.