2023 guinea pigs placed in a circle, where 2022 have a mirror, reflections
Source: 2023 Mathematics Regional Olympiad of Mexico West P6
October 21, 2024
combinatoricscombinatorial geometryreflectiongeometry
Problem Statement
There are guinea pigs placed in a circle, from which everyone except one of them, call it , has a mirror that points towards one of the other guinea pigs. has a lantern that will shoot a light beam towards one of the guinea pigs with a mirror and will reflect to the guinea pig that the mirror is pointing and will keep reflecting with every mirror it reaches. Isaías will re-direct some of the mirrors to point to some other of the guinea pigs. In the worst case scenario, what is the least number of mirrors that need to be re-directed, such that the light beam hits no matter the starting point of the light beam?