iran-konkur 2014 Q143

iran-konkur · Other · konkur-riazi_1393 Number Theory GCD, LCM, and Coprimality
143- We place each of the integers from 1 to 30 on 30 balls and put them in a bag. We draw at least how many balls to be certain that at least two of the drawn numbers have a greatest common divisor greater than 1?
(1) $15$ (2) $11$ (3) $12$ (4) $13$
\textbf{143-} We place each of the integers from 1 to 30 on 30 balls and put them in a bag. We draw at least how many balls to be certain that at least two of the drawn numbers have a greatest common divisor greater than 1?

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(1) $15$ \hfill (2) $11$ \hfill (3) $12$ \hfill (4) $13$

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