A Logic Problem

Given the following equations:

(1) b × c = a + f
(2) a × d = b + c
(3) a × c = b + e
(4) f > e

and a, b, c, d, e, and f are different prime numbers, which one is equal to 2? Give a proof showing why your choice must be 2.

Copyright 2009 All Rights Reserved Rob Dorfman