What direction does the street have on which at noon there is no shadow from the houses?

At astronomical noon, the Sun reaches its highest point in the south. If the houses do not have a shadow, then it is exactly above the street. Depending on the latitude, only the height of the Sun will change. At the equator, it will be exactly at the zenith and we will not be able to tell exactly the direction. At other latitudes, therefore, the street has a north-south direction.