2013 ToT Spring Junior O p3, 11 integer weights
Source:
March 4, 2020
weighingsnumber theorycombinatorics
Problem Statement
Each of weights is weighing an integer number of grams. No two weights are equal. It is known that if all these weights or any group of them are placed on a balance then the side with a larger number of weights is always heavier. Prove that at least one weight is heavier than grams.