## 165. Half-Zombie.

After the trial, Inspector Craig visited a neighboring island. One part of the native population of this island consisted of ordinary people, another of zombies, and the third of so-called half-zombies. The latter included those islanders who had been cursed by sorcerers, but only partially: half-zombies sometimes lied and sometimes told the truth. In the language of the islanders, the words "yes" and "no" were "bal" and "da" (but it was unknown whether "bal" meant agreement or negation). When answering questions, the natives sometimes said "yes" and "no," and sometimes switched to their native language and said "bal" and "da."

Inspector Craig asked one of the natives the following question: "If someone were to ask you whether 'bal' means 'yes' and you decided to answer in your native language, would you say 'bal'?"

The native answered, but Inspector Craig did not record the answer or note in which language it was given. In his notebook, there was only a note that from the received answer, Craig was able to conclude whether the native was a zombie, a half-zombie, or a human.

What did the native answer Inspector Craig and in which language: English or their native language?
165. The only one of the four possible answers ("bal", "yes", "yes", and "no") that neither a human nor a zombie could give is "no." Indeed, if the native were either a human or a zombie and answered Inspector Craig in English, he would have to say "yes." If he answered in his native language, then if "bal" means "yes," he would say "bal" (regardless of whether he is a human or a zombie), and if "bal" means "no," he would say "yes." (I leave the proof of these statements to the reader.) Therefore, receiving any answer other than "no," Inspector Craig could not have determined who the native was. Since the inspector was able to determine who the native was, the answer he received must have been "no," and the native was a half-zombie.