12 stones with integer weight (2021 Auckland MO J5)
Source:
November 14, 2021
combinatoricsnumber theory
Problem Statement
There are stones each of which weighs an integer number of grams. It is known that any of them can be put on two pans of a balance scale, six on each pan, so that they are in equilibrium (i.e., each pan will carry an equal total weight). Prove that either all stones weigh an even number of grams or all stones weigh an odd number of grams.