An annoyed teacher asked her student to do the following: (1) Start with the number 12. Go to step (2). (2) Take the negative of
the number reached at the end of the previous step. Go to step (3). (3) Add 1 to the number reached at the end of the previous step. Go to step (4). (4) Go back to step (2) unless you have already gone through step (3) a hundred times; if you have gone through step (3) a hundred times already, tell the teacher the last number you reached. To the teacher's surprise, the student gave her the correct final answer within a minute. What was it?
