And a follow-up to my "guess my number" riddle. I thought of it a while back but I am not actually sure of the answer.
I am thinking of an integer between 1 and n inclusive (assume you know n when you are asking). You can ask me any three yes or no questions this time, but the following things are changed:
1) Instead of answering yes or no, I will instead respond by raising my left or right hand. One means yes and one means no, but you don't know which is which to start.
2) If you ask a question I cannot answer truthfully, instead of remaining silent, I will either answer the yes or no question with either the choice with the larger probability of being true, or that with the smaller probability. I will answer all ambiguous questions consistently also; that is, I will ALWAYS give either the larger or smaller probability answer, but you again do not know which to start. If you ask a question with a 50/50 chance of being yes or no, I'll answer randomly.
What is the largest n for which there exists a definite system to always guess my number correctly? n = 4 is pretty trivial (ask factual question, do binary search), but is it possible for n>4? I get this feeling it isn't, but I mean