numbers on faces of a pyramid with base 2013-gon
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2013 Shortlist LRP1 day1 (LRP = Logical Reasoning Probability)
September 26, 2021
combinatorics
Problem Statement
Consider a pyramid whose base is a -sided polygon. On each face of the pyramid the number is written. The following operation is carried out: a vertex is chosen from the pyramid and add or subtract from all the faces that contain that vertex. It's possible, after repeating a finite number of times the previous procedure, that all the faces of the pyramid have the number written?