5-103. Mr. Q is such a mean teacher! The next time Mathias gets in trouble, Mr. Q has designed a special detention for him. Mathias will have to go out into the hall and stand exactly 100 meters
away from the exit door and pause for 1 minute. After every 1 minute pause he is allowed to walk
exactly halfway toward the exit. Mr. Q says that when Mathias reaches the door he can leave,
but he cannot break the halfway rule (even by a tiny amount).
When can Mathias leave? Show work to support your answer.