Problem 2
Source: Danube Mathematical Competition 2017, Romania
October 28, 2017
combinatorics
Problem Statement
Let n be a positive interger. Let n real numbers be wrote on a paper. We call a "transformation" :choosing 2 numbers and replace both of them with . Find all n for which after a finite number of transformations and any n real numbers, we can have the same number written n times on the paper.