Problem #PRU-116560

Problemas Métodos Principio extremal Principio extremal (otro) Principio del casillero Principio del casillero (otro) Demostración por contradicción

Problem

2011 numbers are written on a blackboard. It turns out that the sum of any of these written numbers is also one of the written numbers. What is the minimum number of zeroes within this set of 2011 numbers?