set of n numbered lights
Source: 2011 Portugal (OPM) p3
May 20, 2024
combinatorics
Problem Statement
A set of lights, numbered to , are initially off. At every moment, it is possible to perform one of the following operations:
change the state of lamp ,
change the state of lamp , as long as lamp is on,
change the state of lamp , as long as lamp is on and all lamps are off.
It shows that it is possible, after a certain number of operations, to have only the lamp left on.