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There are two species living in the land of Puzzling: elephants and dinosaurs.

Elephants always tell the truth when talking about an elephant, but always lie when talking about a dinosaur. Dinosaurs always tell the truth when talking about a dinosaur but always lie when talking about an elephant.

(Note that 'Dumbo is an elephant' is a statement about Dumbo.)

Challenge 1:
John says, "Zayin is a dinosaur." What species are John and Zayin?

Challenge 2:
Tom says that Judith says that Margaret says that Elly is an elephant.
What species are Tom, Judith, Margaret, and Elly?

Challenge 3:
There are $N$ creatures ($N\ge3$) sitting around a round table. Everyone tells their right-hand neighbor, "You lie about your right-hand neighbor." What are the valid values for $N$? How are the animals arranged around the table?

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If John is a dinosaur, he will say that a dinosaur is a dinosaur (true) and an elephant is a dinosaur (lie.) If John is an elephant, he will say that an elephant is an elephant (true) and a dinosaur is an elephant (lie.) Therefore all we can establish from John says "Zayin is a dinosaur." is that John is a dinosaur.

There are 16 combinations of animals for the second part. For example TD JD MD ED would mean all 4 are dinosaurs. Since they would each tell the truth, starting with M saying "E is a D", you end up with T saying "E is a D" which is not what was said, so that combination can be ruled out.

There are more than 1 combinations that lead to the sentence being uttered though: for example TE JD MD ED would make M say "E is a D" truthfully, and J pass that along truthfully, but then T lie and report the chain ended E. Similarly TD JE MD ED would start with M saying "E is a D" but then J would lie, claiming M said E was an E, and then T would pass that along truthfully. I haven't tested all 16 combinations, but my suspicion is that whenever you have an odd split (1-3 or 3-1) of animal types, that is the sentence that will be uttered.

For the third part, the sentence "you lie about your righthand neighbour" involves 3 animals: the speaker S, the subject Y, and the neighbour N. There are 8 combinations possible: DDD, DEE, DED, DDE, EEE, EED, EDE, EED. In the 4 cases where Y and N are different, Y really does lie, but only if S and Y are the same will S say so. In the other 4 cases, Y tells the truth, but if S and Y are different S will lie about that. So the patterns DEE, DDE, EED, and EDD will lead to this sentence. You can get this pattern if they sit in pairs - for example four of them as DDEE with the final E "looping back around" and sitting next to the first D. The total number of animals must be a multiple of 4 to reuse this pattern, eg DDEEDDEE and so on.

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  • $\begingroup$ Kate, I really appreciate your approach to this question, I wanted to ask you what would a problem like this come under? Mathematical logic? $\endgroup$ – user99088 Nov 5 '15 at 14:02
  • $\begingroup$ Did you make this puzzle up yourself? Do you know the answers? Were you expecting two of the three answers to be "you can't determine that"? Generally that's not a super satisfying solution to a puzzle. $\endgroup$ – Kate Gregory Nov 5 '15 at 14:30
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    $\begingroup$ No I didn't expect two answers to be undeterminable but I appreciated it because your the first person on here not to brush me off saying its for home work etc. $\endgroup$ – user99088 Nov 5 '15 at 14:31
  • $\begingroup$ Well, looking at the first revision, I would say that it is homework after all. Which doesn't make it off topic, but you can't just post your question as is and get others to solve it for you. It would have been better to ask specifically about what you were stuck on, or to ask if your solution or approach was right. People have since edited it to be a better puzzle for this site, but they lost information in doing so. Revision 1 fits this answer better and if it was your homework, it contained clues to help you solve it. I hope you can understand this kind of logic better now. $\endgroup$ – Kate Gregory Nov 5 '15 at 14:41
  • $\begingroup$ Definitely! I apologise for inconvenience $\endgroup$ – user99088 Nov 5 '15 at 14:44

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