All the Math in the World...

I have a minor in applied mathematics, which I received along with my bachelor's in Nuclear Engineering at Michigan.  Since then, I've taken more math classes.  I like math.  I'm good at math, and I feel like I've taken most (if not all) of the applicable math courses that I should need to solve all the problems I'll run into in the future.

Apparently not!


First evidence of this: last week's puzzler on Car Talk (I podcast it).

The problem: 'how far apart are two 100' tall telephone poles if the 150' line between their tops droops down to 25' above the ground?'

My answer:  I used hyperbolic trigonometry to prove 126' apart.  I've known for a long time that hyperbolic cosine defines how telephone/electric wires droop (it's one of the few real-world applications), and this was the first time that I looked up the equations to figure out how.  It wasn't too hard, and I felt really accomplished as I submitted it to the Car Talk website with the full mathematical explanation.

The real answer: They'd have to be touching.  75' is half the length of the line, and the line has to droop 75'.  Math clouded up my ability to see the trick in the question.


Second evidence of this: trying to form the schedule for Easter games.

The problem: There are 10 teams.  There are 4 games.  One game requires 4 teams, the other 3 games require 2 teams.  Design a schedule so that all teams get to play all games, but they have to play the game that requires 4 teams twice (so 5 total rounds).  Also, no two teams play with or against each other more than once.  (You may have seen this on facebook if you are friends with me.)

My answer:  Hours upon hours of spreadsheets, drawing scenarios on paper, and even chopping up a bunch of pieces of paper and moving things around on my coffee table lead to no solution.  I would not accept that it wasn't possible.  There seemed to be too many combinations for this not to be possible.  At the last minute I was able to make it so that nobody played the same team twice in the 3 games that require 2 teams, but there were some of the same matchups in the 4-team game.  At one point, Annie caught me writing out ratios of factorials to try and determine the number of permutations of this scenario (which I failed to find since not all of the permutations were the same length).

The real answer:  It's not possible.  I still can't prove this mathematically, but Annie and I methodically approached this problem from every angle, without success.  So, until I'm proven otherwise (and I'm not going to prove myself wrong), the scenario wanted doesn't work.  I wish I had known this beforehand.  It would have saved me hours of my life that I'll never get back.

U + Me = Us.  [At least] I know my Calculus,
~RoB