System of Equations

Quickly solve this system of equations:

x - y = 5
x^2 - y^2 = 35

Objects

There are 50 distinct objects lying on a table. I can choose any of the objects, and any of the objects can choose me. How many ways are there to pick the objects?

Counting Divisors

If n is the perfect cube of a natural number and has 28 divisors, 2 of which are prime, how many divisors does the cube root of n have?
(Source: Art of Problem Solving: Introduction to Number Theory)