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We do say "he is not stupid." What follows ‘not’ should be an adjective - in this case ‘stupid’. ‘Fool’ is not an adjective but a noun. You should answer ‘no fool’ or ‘not a fool’ but not ‘not fool’. If the word ‘foolish’ (adjective) had been in the question, you would have answered correctly with ‘not’.
We do say "he is not stupid." What follows ‘not’ should be an adjective - in this case ‘stupid’. ‘Fool’ is not an adjective but a noun. You should answer ‘no fool’ or ‘not a fool’ but not ‘not fool’. If the word ‘foolish’ (adjective) had been in the question, you would have answered correctly with ‘not’.
no instead of not 
Re: no instead of not 
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