Problem 1: 2 Feet or 2 Miles

 -- Turned out to be difficult (in an annoying way) than I had intended.
    you have to compute the distance from the old to the new point.
    I put in the special note just to point out that you can do this
    by avoiding the floating point numbers.  You can do it by using
    the sqrt, but you don't have to.

Problem 2: New Math

 -- I first saw the clip shortly after last year's contest and thought 
    it would make for spiffy problem.  I kept all the integers positive (e.g.,
    non-zero) to avoid the subtle math questions about whether 0 is
    an additive identity anymore and so on.  (10 + 0 = 10 or 1?)
    There's also annoying questions about the inconsistency of the
    addition operator.  20 + 5 = 7 in this messed up system, yet
    when adding 5 14's together, you get 20+5 = 25.  Like Zeke
    said, don't overthink it.

    Anyway the "math" ignores powers of 10.  You just sum the digits.

Problem 3: Fast Exponentiation

 -- Sometimes authors try to lead you astray by describing a solution
    to a problem that will never work.  This is not one of those
    cases.  The problem literally tells you how to solve it, even
    going so far as to provide the information on modular arithmetic
    to keep things well bounded.  

 -- Some folks tried to do this by computing a^n and then taking the mod.
    That will not work.  You'll hit an overflow.  Things like
    2147483647^2147483647 will overflow everything but real long integer
    abstract packages.  You really do have to do this by using the 
    result (given in the problem) a*b (mod p) = (a mod p) * (b mod p) (mod p).

 -- Also: you need to do an `a = a % p' to start things out.  Remember,
    a could be any number within 2^31.  p only goes up to 2^15.  If
    you do not do the mod, the first multiplication could require
    62 bits to fit the answer (which will mess up everything else
    later).

 -- The upper limit on squarings and multiplies is 2 * log2 (n).  You'll
    get log2 (n) squarings and may get log2 (n) multiplies for the odd
    powers.  



Problem 4: Football Scoring

 -- My intention was to create a problem that makes use of memoization.
    The bit about "order matters" was to make the problem easier (I think).
    If order doesn't matter, then things get complicated because
    of overcounting and memoization goes out the door.

Problem 5: NOWHERE Postal Service

 -- Graph reachability.  From any node, check what other nodes you
    can reach.  All those nodes are in a group.  (The edges are
    non-directional.  If they weren't, there would be some funniness
    about how you define a group of CPOs.)


Problem 6: Supercomputer Job Scheduling

 -- This is a bit time consuming.  I hope you worked on the other
    problems before trying this one.  I actually had intended to give a
    different version of this problem but that one got out of hand
    quickly.  (Actually, that version would be a spiffy data
    structures class project someday, but it was insane for a 3
    hour contest.)  I think the scaled back version worked well
    for this contest.