Puzzle—Brushing the Court Lines Optimally

Clay-court tennis players are familiar with the well-known courtesy, after finishing their match, of preparing the court for the next players who will use the court. Preparation consists of two parts: sweeping the court and brushing the lines. Sweeping the court is straightforward, but the quantitatively oriented player surely wants to know how to brush the lines (a nontrivial routing problem) in the most efficient fashion.