MathDB

LRP1

Part of 2013 Costa Rica - Final Round

Problems(1)

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)

9/26/2021
Consider a pyramid whose base is a 20132013-sided polygon. On each face of the pyramid the number 00 is written. The following operation is carried out: a vertex is chosen from the pyramid and add or subtract 11 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 11 written?
combinatorics