A traveller starts from the black town and wishes to go as far as possible while making only fifteen turnings and never going along the same road twice. 
The towns are supposed to be a mile apart. 
Supposing, for example, that he went straight to A, then straight to B, then to C, D, E, and F, you will then find that he has travelled thirty-seven miles in five turnings.

How far can he go in fifteen turnings?

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Math Genius