# 2007 IMO Problems/Problem 6

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## Problem

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

## Solution

Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.

 2007 IMO (Problems) • Resources Preceded byProblem 5 1 • 2 • 3 • 4 • 5 • 6 Followed byProblem 6 All IMO Problems and Solutions
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