In America they make use of ZIP (Zoning Improvement Plan) codes to help direct mail. Each city/town makes use of a 5-digit code (we shall ignore ZIP+4 codes); for example, Hillsgrove, Pennslyvania, is 18619.
However, due to rotational symmetry certain codes, like the one used for Hillsgrove are detour-prone, as they could be read as a different code upside down. As a result, 61981 (Hillsgrove's ZIP code read upside down) is not used.
How many 5-digit ZIP codes are detour-prone?