4.50 The street map of a city is a $5 \times 5$ grid, where there is a snowplow at point $A$. Find the length of the shortest route that covers all streets and returns to the starting point.
[Solution] Clearly, there are 60 segments of length 1 in the graph, but there are 16 odd vertices, i.e., the 16 boundary nodes in the grid table excluding the 4 corner points. Since they can be divided into 8 pairs, at least 8 segments of the path have to be walked twice. Therefore, the length of any circuit that sweeps through all the streets is at least 68.

On the other hand, when following the broken line $A B C D E F G H I J L M N O P Q A R S T A$ to clear the snow, the length of the route taken is exactly 68. Hence, the length of the shortest route is 68.