MathDB
At least 32 points inside a cube

Source:

September 13, 2010
geometry3D geometryinequalitiescombinatorics unsolvedcombinatorics

Problem Statement

Suppose that 19851985 points are given inside a unit cube. Show that one can always choose 3232 of them in such a way that every (possibly degenerate) closed polygon with these points as vertices has a total length of less than 83.8 \sqrt 3.
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