k-man

Similarly, the number of zeroes in the second range is SUMn=[2,1181](9*10n-2*(n-1)) + 1181, so they are the same.

Guilty. I didn't consider edge cases at all and assumed that all the numbers are distinct.

Well, I suppose you could say that it implicitly relies on Bayesian analysis in a way that I just don't draw attention to in this approach. Nice! However, I think either due to the precision or a mistake somewhere your result is a bit off.

Your analysis isn't wrong; doing it like that won't work. Try another approach.

I'm ready to hear your solution.

Ignore my previous post as I found an error in my calculations and this time I think I found the maximum.

I don't know if I'm taking your hints correctly, but based on your hints, I'm inclined to interpret "infinity" as "no specific limit, but within some practical boundaries". Using this interpretation I can suggest a...

here is an example of 2/6 ratio. Only ABC' and A'B'C triangles are obtuse. Others are acute.

koren, This solution uses the deterministic nature of truth tellers and liars and non-deterministic nature of a random answerer. For any question that has a definitive yes/no answer (e.g. "Is 1+1=2?") both truth tellers and liars can know ahead of time what their answer will be and they can either tell the truth or lie about it. However, a random answerer cannot predict his future behavior, so he cannot answer a question about his next response. Again, as bonanova said, that's based on the assumption that random first determines the true answer to the question and then decides whether to tell the truth or lie. So, if R is asked "will your second answer to this question be the same as your first answer?" he will fail to determine the truth value and show a white light. Now, in your last post, you're suggesting that R assumes either T or L before a question is even asked and then answers the question as T or L would. That's a different behavior and will require a different solution, but R acting as T or L can still produce different answers than T or L would. So, can you clarify the behavior of Random?