Number theory · Divisibility rules · Digits of an integer · Greatest common divisor · Casework · Constructions
A teacher handed Matej four sheets of paper, each carrying one nonzero digit. Matej laid the sheets in a row and so formed a four-digit number. He then interchanged two of the sheets, without flipping or rotating either of them, and so formed a second four-digit number.
Whatever digits were written on the sheets, could he have formed two numbers that are not relatively prime?
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2010, 1. letnik, category A, problem 4. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source