13 with integer weights (2021 Auckland MO S5)
Source:
November 15, 2021
combinatorics
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 all stones weigh the same number of grams.