
MOP 2001 Poetry
Last year it was song writing, and this year one MOPper took up poetry. Here are two poems that Steve Byrnes wrote for Team Contest #1.
Steve Byrnes' Poetry Proof
Problem: Do there exist four quadratic polynomials such that if you put them in any order, there exists a number such that the values of the polynomials at that number, in the chosen order, are strictly increasing? (Team contest #1, problem 1)
We can put them in order a number of ways,
The parabolas four which the problem portrays;
That number of ways, as we see is quite plenty:
Factorial function of four  four and twenty!
But each pair of parabolas (this is quite nice)
Intersect with each other, at very most, twice.
To see this, first note that if two coincided,
It'd break a condition the problem provided.
For at any number, as we ascertain,
They can't strictly increase, when some two are the same.
The degree of their difference, it's easy to see,
Is just two, one, or zero, but not ever three.
Their difference is zero when they intersect:
In at most the two roots, just as we should expect.
There are six, four choose two, pairs of curves, which then makes
At most twelve intersections. That's all it takes,
For the order can change in just these dozen places,
Or possibly fewer. In all of these cases,
At most, they are ordered in ways 10 and 3
Which is less than the twentyfour we need, QED!
Steve Byrnes' "Ode to Anders"
(During the same team contest, after Anders stole the above problem.)
Watch out for Anders, 'cause Anders is mean;
The meaniest meanie that you've ever seen.
The meanies of Meanville will all just turn green
Out of envy for Anders, the meanest of mean.
