IMO Shortlist 1983 problem 13


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2. travnja 2012.
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Let E be the set of 1983^3 points of the space \mathbb R^3 all three of whose coordinates are integers between 0 and 1982 (including 0 and 1982). A coloring of E is a map from E to the set {red, blue}. How many colorings of E are there satisfying the following property: The number of red vertices among the 8 vertices of any right-angled parallelepiped is a multiple of 4 ?
Izvor: Međunarodna matematička olimpijada, shortlist 1983