## Subject III. (20 points)

The natural numbers $1, 2, 3, \ldots, 2013$ are written on cards, with the written side facing down. We say that a card is "lucky" if the number written on it is divisible by 20 or 13. What is the smallest number of cards that must be turned over, without looking, to be sure that at least one of them is "lucky"?

Prof. Sorin Borodi, Alexandru Papiu Ilarian Theoretical High School, Dej