The Island of Tycos

Once upon a time two ships from the allied states of Cos and Tyros were travelling in convoy when they were seized by a sudden storm and swept far out into Thassa where, severely damaged, they were cast ashore on an uncharted island and wrecked. Their passengers were able to found a successful colony on the island, which they named "Tycos", and over time their numbers grew.

After several years they were all stricken down by a strange brain fever. Not one islander escaped. Fortunately, it was not life-threatening nor especially debilitating, but the effects were persistent even after the acute stage of the fever was over. It caused recurring attacks of delirium and warped the sufferer's perception of reality. Bizarrely, it turned out that those of Cosian descent, when delirious, believed the exact opposite of what was true, but when they were lucid, whatever they believed was true. Even more strangely, those of Tyrosian descent believed falsehood when they were lucid, but truth when they were delirious.

1. A Tycosian once believed he was of Cosian descent. Do we know whether this was true? Can we tell if he was delirious or lucid?
2. A Tycosian once believed he was delirious. Do we know whether this was true? Can we tell if he was Cosian or Tyrosian?
3. A Tycosian once believed he was lucid. A few Ahn later, he either suffered a fresh attack of delirium, or the one he was already suffering ceased, and he then believed he was Tyrosian. What was his lineage, and his condition at this time?

Tycos, like its parent states, had a unique Ubar all of its own, but after the brain fever epidemic there was, unsurprisingly, considerable confusion as to the identity of the Ubar. Enquiries, of course, led nowhere. In a suitable mental state, a man might believe anyone was the Ubar; and if a general enquiry were held, a man in the grip of delusion might believe the results of the enquiry had been anything, no matter what they actually had been.

One day, a man called Bortus was thinking very hard about this matter and he came to the conclusion that if he was a lucid Cosian then he himself was the Ubar. Meanwhile, a man called Kortus was thinking equally hard about the same question. He concluded that if he, Kortus, was either a lucid Cosian or a delirious Tyrosian then he himself was the Ubar. At this time Bortus and Kortus were either both lucid or both delirious.

Was either of them right? Which one, if so? Were they lucid or delirious?