A long time ago, there existed Martians with 3 different colours: red, green and blue. As Mars was devastated by an intergalactic war, only 2 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 2022 red Martians, 2022 green Martians and 2022 blue Martians?b) Is it possible that, after using that machine finitely many times, we have 2021 red Martians, 2022 green Martians and 2023 blue Martians? combinatoricsnumber theory