We present a very short survey of known results and many new estimates and results on the maximum number of points that can
be chosen in the n-dimensional unit cube so that every distance between them is at least 1.
We give a very short survey of the results on placing of points into the unit n-dimensional cube with mutual distances at least one. The main result is that into the 5-dimensional unit cube there can be
placed no more than 40 points.
We remind some old packing problems, e.g. dense packing of spheres in the more-dimensional unit cube, maximization of the area of the union of triangles packed in the circle, potato bag problems, and briefly summarize the related known results.