Question D.16 in Guy’s Unsolved Problems in Number Theory asks whether one can find arbitrarily many triples of positive integers all of whose sums are equal and whose products are equal. We will present and reinterpret A. Schinzel’s clever proof of this question and show how the natural generalization of his techniques relates to the problem of understanding which rational polynomials have the property that you can vary one of their coefficients and infinitely often the resulting polynomial will split into linear factors over Q. We then translate this problem into a question about understanding branched covers of the projective line whose Galois closures have prescribed arithmetic and geometric properties. We will solve this problem using an assortment of techniques from the Galois theory of function fields and the arithmetic of elliptic curves. This is joint work with Matthew Satriano and Michael Zieve.