A Cube-covering Problem

Yonghui Fan1, Flavio K.Miyazawa2, Yuqin Zhang3
1College of Mathematical Science Tianjin Normal University, Tianjin, 300387, China
2Institute of Computing, University of Campinas Av. Albert Einstein, 1251, 13083-852, Campinas, Brasil
3Department of Mathematics – Tianjin University, 300072, Tianjin, China

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 \(g_3(n)\).