On an island, two types of people live: good and bad. The good ones always tell the truth, the bad ones always lie. Naturally, everyone is either a boy or a girl on the island. Once, two people said the following about each other:

- Ali: We are bad.
- Bali: We are boys.

Determine whether each of them is good and what gender they are!
Solution. Ali cannot be good, because then his statement would not be true. So Ali is bad, but then he does not tell the truth, which means that both are not bad. This means that Bali is good, so both are boys. Therefore, Ali is a bad boy, and Bali is a good boy.