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Found problems: 1

1986 All Soviet Union Mathematical Olympiad, 429
Tags: cube , combinatorics , unit cube , sum , combinatorial geometry
A cube with edge of length $n$ ($n\ge 3$) consists of $n^3$ unit cubes. Prove that it is possible to write different $n^3$ integers on all the unit cubes to provide the zero sum of all integers in the every row parallel to some edge.