This is actually a much more general problem than proving how smart you are.
Pop Quiz: True or False
- The answer to question 2 of this quiz is true. TRUE OR FALSE?
- The answer to question 1 of this quiz is false. TRUE OR FALSE?
I have seen hugely elaborate multiple-question problems along these same lines, that one would need pencil and paper and much patience to unravel.
Also, consider the following question in English:
This is a good movie, isn't it?
Technically speaking, the question in that sentence is formed by seeking a disagreement. Most english speakers understand that if the answer is simply 'No', then the meaning is 'This is not a good movie'. However, it is not uncommon for confusion to arise from a simple yea-or-nay to such a question, and the question often needs to be rephrased with less ambiguity.
In French, German, and Dutch, and presumably many other languages, there is a word that linguists call a contrastive yes (si, doch, and toch respectively). For example, if someone were to say, "That movie wasn't worth paying for, was it?" a french speaker could reply with "Mais si!" if they wished to express their undying love of John Travolta and all he stands for. Si means that you disagree with the negative clause of the speaker.
Thanks to Albert Herring for significant corrections and additional information.
themanwho says I have so far found one linguistics paper that claims that dutch "toch" cannot be used as a contrastive yes referring to the abstract at http://www.linguistik-online.de/13_01/foolen_a.html. If anyone can shed light on Dutch or any other language, please get in touch.