Algebra · Factorisation · Symmetric sums · Cube
A natural number is written on each face of a cube. At every vertex of the cube one writes the product of the numbers on the three faces that meet at that vertex. The eight numbers at the vertices add up to \(70\). What is the sum of the six numbers on the faces?
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2004, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source