Unwanted Zip Codes

Discrete Mathematics Level 5

In a certain country, they make use of ZIP (Zoning Improvement Plan) codes to help direct mail. Each city/town makes use of a 5-digit code (which could start with 0). For example, Rose Hill's ZIP is 18619.

Because certain codes could be interpreted differently when read upside down, they have been marked as unwanted. For example, Rose Hill's ZIP code becomes 61981 when read upside down, hence it is not used.

How many 5-digit ZIP codes are unwanted?

Note: This not an original problem.


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