Weights - TT 2009 Junior-A5
Source:
September 3, 2010
Problem Statement
We have N objects with weights grams. We wish to choose two or more of these objects so that the total weight of the chosen objects is equal to average weight of the remaining objects. Prove that(a) (2 points) if is a perfect square, then the task is possible;(b) (6 points) if the task is possible, then is a perfect square.