[ Mathematical logic (other) $]$

Ponugau. Three parrots gathered - Gosha, Kesh, and Roma. One of them always tells the truth, another always lies, and the third one is a trickster, sometimes telling the truth and sometimes lying. When asked: "Who is Kesh?" - the parrots answered as follows: Gosha: — Kesh is a liar. Kesh: — I am a trickster! Roma: — He is an absolutely honest parrot. Who is the honest parrot, who is the liar, and who is the trickster?

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Notice that Roma cannot be honest

## Solution

Roma cannot be honest, because then Kesh would also be honest, which is impossible. Therefore, Roma is either a liar or a trickster. Let's assume Roma is a liar. Then Kesh is a trickster (he cannot be a liar, as Roma is the liar, and he cannot be honest, as his statement would then be false). But then Gosha must be honest, which contradicts his statement. Therefore, Roma must be a trickster. Then, according to Kesh's statement, Kesh is a liar, and the only possibility left for Gosha is to be honest. His statement is indeed true. And from Roma's statement, it follows that he (Roma) lied in this case. Thus, the honest one is Gosha, the trickster is Roma, and the liar is Kesh.