Question 41
The city of Mar del Plata has a shape of the square $WSEN$. For a given even integer $n$, it is divided by $2(n + 1)$ streets into $n \times n$ blocks (the streets run also around the square). Each block has a size of 100 m x 100 m. All the streets in Mar del Plata are one-way. Each street has one direction along the entire length. Every two adjacent parallel streets have opposite directions. The $WS$ street is directed from $W$ to $S$ and the $WN$ street is directed from $W$ to $N$. A street cleaning car starts at $W$. Its aim is to arrive to $E$ and clean the roads it passes through. What is the length of the longest possible route it can pass if no 100 m segment can be passed more than once? (For $n = 6$, Fig. 1 shows the map of the city and one of the possible, but not the longest, routes of the car. See also http://goo.gl/maps/JAzD.)
Fig. 1
Fig. 1