8.3. On an island, there live knights and liars. Knights always tell the truth, and liars always lie. Some of the island's inhabitants claimed that there is an even number of knights on the island, while all the other inhabitants claimed that there is an odd number of liars on the island. Could there be exactly 2021 inhabitants on this island?
Answer: cannot.

Solution. If the number of island inhabitants is odd, then either there is an even number of knights and an odd number of liars, or an odd number of knights and an even number of liars. In the first case, it turns out that all the islanders told the truth. But then all of them are knights, and the number of knights in this case should be even. In the second case, it turns out that all of them lied. But then all of them are liars, and the number of liars in this case should be even. Thus, both cases are impossible.