I haven't seen this kind of liar type before, so here is a simple puzzle as a means for a trial run. In particular, I did check it myself, but with new mechanics it's easy to miss something (I hope I didn't), so don't be angry if the puzzle doesn't have a proper answer or if it can be easily circumvented.
There are three persons A, B, C. A and B say truths or lies randomly (i.e., they first construct an answer and then they flip it randomly, only yes/no questions, circular dependencies are invalid). C tells the truth or lie depending on whether A and B told truths or lies in their last respective answers, but we don't know how exactly (there are $2^4$ possibile strategies for C). Each time you ask a question, all three answer it in order A B, C. How many yes/no questions do you need to ask to know which of the two roads, left or right, leads to salvation?
Also, any suggestions of improvements are welcome and will be greatly appreciated.
- Just to make it clear, C's strategy is static, i.e., he does not change it. We do not know (at least initially) which one it is, but there is only one that he is using.
- We cannot ask about things that are undecided in the future (for example A's or B's coin flips), but we can ask about things that are fixed, in particular, things that are in the past (it won't create any circular dependencies). To give an example, when C is answering his question, A and B have already said their replies and they cannot change them anymore. In other words, their answers became fixed, and the question could depend on that information, given that it doesn't cause any contradictions or circular dependencies when A and B are answering it.