There are 10 people standing in a circle. Some of them always tell the truth. Some of them always lie. The rest of them sometimes tell the truth and sometimes lie. There is at least 1 of each type of person. When asked if they were standing next to at least 1 truth-teller, all of them responded yes. When asked if they were standing next to only truth-tellers, every other person responded yes and the rest responded with no. Find all possible configurations. (Rotations and reflections do not count as different configurations.)
I have the following been able to find the following information:
- there is at least 3 truth-tellers, they are next to each other
- the liar is not next to any of the truth-tellers
I think that the number of truth-tellers must go up in increments of 3, so I think I only have to test 3 truth-tellers and 6 truth-tellers, but I am not sure if my logic for this is correct.(According to the first question, a truth-teller must be next to at least one more truth-teller, according to the second question, one truth-teller would say Y and the other would say N, meaning the one who says Y must have a truth-teller on both sides. Both these truth-tellers would say N, meaning they can't be next to any more truth-tellers)
What is really throwing me off is the sometimes people, please help.
