IMO 1970 LL POL41

Let a cube of side 1 be given. Prove that there exists a point

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IMO 1970 LL POL41

Origin: POL

Problem

Let a cube of side 1 be given. Prove that there exists a point A on the surface S of the cube such that every point of S can be joined to A by a path on S of length not exceeding 2. Also prove that there is a point of S that cannot be joined with A by a path on S of length less than 2.