Overcomplicated wording for a simple combinatorics problem
Source: Lusophon Mathematical Olympiad 2023 Problem 1
May 27, 2023
combinatoricsnumber theory
Problem Statement
A long time ago, there existed Martians with different colours: red, green and blue. As Mars was devastated by an intergalactic war, only Martians of each colours survived. In order to reconstruct the Martian population, they decided to use a machine that transforms two Martians of distinct colours into four Martians of colour different to the two initial ones. For example, if a red Martian and a blue Martian use the machine, they'll be transformed into four green Martians.a) Is it possible that, after using that machine finitely many times, we have red Martians, green Martians and blue Martians?b) Is it possible that, after using that machine finitely many times, we have red Martians, green Martians and blue Martians?