Article : Pyramids - Colegiul National C. Negruzzi (Iași - Roumanie)

The tower is built of matching cubes, of side 1, stacked one over the other and glued to the corner of a wall.
Calculate the number of cubes used to build a tower of height of 30.
A number n≥3 of cubes placed side by side covers perfectly a square. Calculate the values of n such that we can build a pyramid (as the initial tower) rearranging the cubes, without remaining any unused cubes. For every found value of n calculate the height of the built pyramid.
Build a regular triangular pyramid by overlapping some spheres of diameter 1 (instead of cubes). Calculate the height of such a pyramid formed with 1330 balls.
Find the volume of the minimal tetrahedron in which the pyramid found at point c) can be inscribed.