429

Part of 1986 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 429 All Soviet Union MO 1986 n^3 diff. integers on n^3 unit cubes

Source:

A cube with edge of length

n

n\ge 3

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.

combinatoricscombinatorial geometrycubeunit cubeSum