Balanced Centrifuge Problem

Abstract

A centrifuge is a device used to separate fluids by spinning a collection of test tubes at high speed. Since it spins very fast, it is important that the center of the mass of the test tube is at the center of the machine to avoid extra stress on the machine. In this talk, we will discuss if it is possible to balance $k$ identical test tubes in an $n$-holed centrifuge, and related math problems.