Problem1:

Let T be a convex 3-D body with the volume V. Let L1, L2, L3 be the lengths of projections of T onto any three orthogonal lines. Let S1, S2, S3 be the areas of 2-D projections of T onto any three orthogonal planes.

Problem2:

Let P be the regular polygon with N>2 vertices. If we need to build a closed tour of shortest length that touches each polygon's side at least once, how such a tour can be found?