A Cube-covering Problem

Abstract

We consider the problem of covering a unit cube with smaller cubes. The size of a cube is given by its side length and the size of a covering is the total size of the cubes used to cover the unit cube. We denote by $g_3(n)$ the smallest size of a minimal covering using $n$ cubes. We present tight results for the upper and lower bounds of $g_3(n)$.