DE-BUNDESWETTBEWERB 2014 Problem 1
Anja has to write integers on the board such that arithmetic mean of any of the three numbers is among those numbers. Show that this is possible only when she writes nothing but equal integers.
Dataset text AI-MO AoPS. Quoted with source.
Official text: Bundeswettbewerb Mathematik 2014 official paper, page 1.
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