Minimum Bucket and Car Battery Problems

Abstract

A solar car needs 5 fully charged batteries to run, and it depletes those batteries in 5 hours. The batteries are rechargeable, and solar panels on the car are able to charge 3 batteries simultaneously. It takes 3 hours for the solar panels to finish charging 3 batteries. Furthermore, batteries cannot be charging and in use at the same time. If the car always starts running as soon as 5 full batteries are available, and the solar panels can only operate if 3 empty batteries are available, how many batteries are needed so that the car can eventually run without stopping? We investigate this resource optimization problem and its different variations.