Distinguishing sum-set from product-set
Source: Tournament of Towns 2016 Fall Tour, A Senior, Problem #4
April 22, 2017
algebra
Problem Statement
There are red and blue cards each having a number written on it. For some distinct positive real numbers, it is known that the set of numbers on cards of a particular color happens to be the set of their pairwise sums and the other happens to be the set of their pairwise products. Can we necessarily determine which color corresponds to sum and which to product?(B. Frenkin)(Translated from [url=http://sasja.shap.homedns.org/Turniry/TG/index.html]here.)