Spring 2001  CS100M  Bonus Exercise E4: Story Power     due online 2/15

You should spend at least 30 to 60 minutes thinking about it, but this
exercise is purely bonus --no core points-- so don't worry if you
can't figure it out.

Consider this variation on the bonus from P1:

Suppose Alan, the TA, performed the following algorithm at one of the
joint CS100J&CS100M software demos:

    While there are 2 or more CS100 students
        Pick 2 students at random.
        If they are from the same class (both J or both M) then
            They both leave.
            A J student enters.
        If they are from different classes (one J and one M) then
            The M student stays.
            The J student leaves.

(In the original bonus, the J student stays, M student leaves.)

Observe that at each step, the number of CS100 students goes down by
exactly one.  

1. Let m = initial number of M students.
   Let j = initial number of J students.
   Assume m+j >= 1.

   What, if anything, can be said about the last CS100 student left in
   the room?  

   Length limit on your answer: 3 lines of at most 75 characters per line.
   (Our solution is 1 line.)

2. Briefly but clearly justify your answer.  

   Length limit on your answer: 8 lines of at most 75 characters per line.
   (Our solution is 4 lines.)
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[2/12] Submission: submit online.  Follow the instructions at:

    http://submit.cs.cornell.edu/cs100m-ex/instructions.html