Combinatorics · Counting · Positions in a line · Parity · Divisibility · Bounding
Every school of a certain region sent exactly \(3\) students to a competition, and Andrej, Blaz and Zan all came from the same school. When the competitors lined up to collect their starting numbers, Andrej noticed that the number of competitors standing in front of him was equal to the number standing behind him. Both of his schoolmates were behind him in the line: Blaz stood in place \(19\) and Zan in place \(28\). How many schools took part in the competition?
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2009, 1. letnik, category A, problem 5. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source