IMO Shortlist 2007 problem A7


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2. travnja 2012.
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Let n be a positive integer. Consider
S = \left\{ (x,y,z) \mid x,y,z \in \{ 0, 1, \ldots, n\}, x + y + z > 0 \right \}
as a set of (n + 1)^{3} - 1 points in the three-dimensional space. Determine the smallest possible number of planes, the union of which contains S but does not include (0,0,0).

Author: Gerhard Wöginger, Netherlands
Izvor: Međunarodna matematička olimpijada, shortlist 2007