[ $\left.\quad \begin{array}{ll}\text { Evenness and Oddness } & \\ \text { [ } & \text { Degree of a vertex }\end{array}\right]$

On an island, there live liars who always lie and knights who always tell the truth. Each of them made two statements: 1) "Among my friends, there is an odd number of knights"; 2) "Among my friends, there is an even number of liars." Is the number of islanders even or odd?

#
Regardless of who utters the two phrases, whether a knight or a liar, this resident has an odd number of friends. Indeed, both phrases are either simultaneously true or false, so in either case, the number of friends is the sum of an even and an odd number.

According to problem $\underline{87972}$, the number of vertices of odd degree is even. Therefore, the number of residents on the island is even.

## Answer

Even.