In a Ted-Ed video, Brilliant is promoted with a problem about Ron and Harry. To know the solution, you have to come here to brilliant.org. The problem is the following:
"Harry and Ron told me separately how many times they watched the movie Titanic. I told them "you guys both watched it, but one of you watched it once more than the other". Then they had the following conversation:
Harry: Did you watch Titanic more than I did? Ron: I have no idea. Harry: Me neither. Do you know now? Ron: Yes, indeed! Harry: Really? Then so do I!
What is the sum of the possible number of times Ron watched Titanic?" End of the problem.
The solution says that the sum is 5, which means that one of them has watched it 2 times and the other, 3. But I do not agree with the solution, and this is the reason:
Let's assume that Harry has watched it twice and Ron 3 times. If that's the case, Harry knows Ron could have watched it either 1 time or 3 times. After the first question, Ron replies that he doesn't know, which means that the option where Ron have watched the film once is not true (as he would have replied that he didn't watched it more than Harry), which leads Harry to know that the only possible option is that Ron had watched it 3 times. And if that is the case, then he would have said: —I do know! — Instead of replying: —Me neither.
If we go with the other hypothesis; Harry has watched it 3 times and Ron twice. Ron knows that Harry has watched the film either 1 time or three times, so when Harry asked if Ron have watched it more than him, he can assume that Harry haven't watched the film just once as Harry wouldn't have had the need of asking because he would have known the answer. That is why Ron can assume that Harry has watched it 3 times; being ron's answer: I do know. Instead of: I have no idea.
If we follow this line of thinking (similar to the famous black and white hats problem) we can realize that the correct answer is 7, having them watched Titanic 3 and 4 times. Not 2 and 3.