A fun logic puzzle I ran across. More here. Enjoy!
On the island of Numeria each of the natives is one of two types: Truth-Tellers who always tell the truth, or Liars who never tell the truth. The island is governed by a Council of Elders who will only answer questions that have numerical answers. In fact the only answers they give are whole numbers, either zero or positive. Furthermore, they will never give an answer greater than the current number of council members. This number can vary daily, but is never less than 4 or more than 40. Also, the Council will only answer questions whose correct answer is independent of who is asked (e.g., no questions such as "How old are you?").
One day three native students, Ann, Bob, and Cal, were given an assignment by their teacher to question the council. They each asked a question, which was answered by every council member. Afterward they reported to their teacher and made the following statements:
(1) Ann: I asked the council how many of them were Truth-Tellers.
(2) Bob: I asked the council how many of them were Liars.
(3) Cal: Those statements are not both true!
(4) Ann: All of the answers I received were different.
(5) Bob: All of the answers I received were different.
(6) Cal: At least two of my answers were different.
(7) Ann: The sum of my answers is a palindrome.
(8) Bob: The sum of my answers is a palindrome.
(9) Cal: The square root of the sum of my answers is not less than the number of council members.
What was the number of council members on that day?
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