Q:

A Box of Puzzle Blocks

A cubical box is required to contain a set of wooden blocks (N right parallelepiped solids that fits in without spaces) which have different edges and colors. No two blocks have the same edge linear measurement. All blocks have unique dimension (integer units), thus no square faces. 

What are the smallest box's inside dimensions SxSxS  ?

A:

 4x4x4

Because

 Given there was no constraint to the number of right parallelepipeds, I chose two. Since each solid has pairwise unique side length (and it was not specified that we could not have repeats between solids), the solids in the box have dimension 1x2x3 and 1x2x4. These clearly fit within a 4x4x4 box. 

And if side length is pairwise unique between all solids,

 7x7x7 with solids 1x2x3 and 4x5x6, which again clearly fit. (Originally said 6x6x6, derp.)

