I wouldn't say these sentences are wrong, but most of them would work better using 'neither' instead of 'both'. The 2nd and 3rd sentences really jump out at me in this regard:
2) Neither makes any sense.
3) Neither of you are clever enough for me.
Before anybody asks: although purists will claim that we need a singular verb there, 'are' is perfectly acceptable to most native speakers these days.
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