Problem #PRU-77892

Problemas Matemáticas Discretas Combinatoria Problemas de Pintura Métodos Principio del Casillero Principio del Casillero (otro) Demostración por Contradicción Problemas Divertidos Problemas de Palabras Tablas y Torneos Tablas y Torneos (otro)

Problem

There are 13 weights, each weighing an integer number of grams. It is known that any 12 of them can be divided into two cups of weights, six weights on each one, which will come to equilibrium. Prove that all the weights have the same weight.