2. Each Martian has three hands. Can 2021 Martians hold hands in such a way that each Martian uses all three hands? Each Martian can hold only one hand of another Martian with one of their hands.
Solution. In total, there are $2021 \cdot 3=6063$ hands - an odd number. If they were to hold hands, the hands would be paired (each pair consisting of two hands shaking each other), which is impossible. Answer: They cannot.