3

Part of 1994 Putnam

Problems(2)

Source:

Show that if the points of an isosceles right triangle of side length

1

are each colored with one of four colors, then there must be two points of the same color which are at least a distance

2-\sqrt 2

Putnamcollege contests

Source:

Find the set of all real numbers

k

with the following property: For any positive, differentiable function

f

that satisfies f^{\prime}(x) > f(x) for all

x,

there is some number

N

f(x) > e^{kx}

x > N.

Putnamfunctioncollege contests