Question 16
A teacher gives Matej four pieces of paper, each containing a non-zero digit. Matej arranges them in a line thus forming a four-digit number. He then exchanges two of the pieces (without flipping or rotating them in the process) to form another four-digit number. Can he always do this in such a way that the two numbers he obtains are not relatively prime regardless of the digits that were written on the pieces of paper?