On the next day I came across a native who made a certain statement. I thought for a moment and said: "You know, if you hadn't made that statement, I could have believed it! Before you said it, I had no idea whether it was true or not, nor did I have any prior knowledge that you are a knave. But now that you have said it, I know that it must be false and that you are a knave."(Source: To Mock a Mockingbird and Other Logic Puzzles: Including an Amazing Adventure in Combinatory Logic by Raymond Smullyan)
Can you supply a statement that could fulfill those two conditions? Note: The statement "Two plus two is five" won't work; I would have already known that statement to be false before he made it.
The solution I came up with, which is very similar to what Smullyan described one of his students coming up with in the solutions, is "I will not say anything to you". (The solution suggested was "I am mute".)
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